Did any Apostolic or Ante-Nicene Fathers believe that Jesus was a created being?

Yes, Arius. From his letter to Eusebius of Nicomedia:

But we say and believe and have taught, and do teach, that the Son is not unbegotten, nor in any way part of the unbegotten; and that he does not derive his subsistence from any matter; but that by his own will and counsel he has subsisted before time and before ages as perfect as God, only begotten and unchangeable, and that before he was begotten, or created, or purposed, or established, he was not. For he was not unbegotten. We are persecuted because we say that the Son has a beginning but that God is without beginning.

The teachings of Arius were the principal controversy that led to the council of Nicea, where Arius' views were emphatically rejected (at least 3 concepts of Deity were considered by the council, and Arius' views were dead last in terms of support).

Very little of Arius' teachings survive today because the church considered them heretical and was very keen on eliminating them.

Source

Addendum

For reasons that remain unclear to me, this post about history has elicited some surprisingly un-Christian responses. FWIW, I decidedly reject the teachings of Arian.

To those who suggest he should be disqualified as a church Father because of heresy, that's an understandable position to take. But to be logically consistent, we'd have to disqualify a considerable number of other church Fathers as well.

The Shepard of Hermas (SH) was accepted by many to be divine or on par with scripture. It may be found in the Sinaiticus manuscript.

So, how did the book have enough sway that writers such as Origen and Didymus the Blind quoted it as Scripture while others like Terullian claimed that it was “universally rejected” (On Purity, Chap 10)? The Shepherd likely was thought to occupy some sort of inspired middle ground. Clement of Alexandria wrote that “it is in a divine manner that the power which spoke to Hermas by revelation.” Simply put, it was considered prophetic, though maybe not quite up to par with real Scripture. Just as the Deuterocanon was thought to be perhaps inspired but not quite written by God through prophets, the Shepherd might have been a similar, post-Apostolic analogue in the minds of some. -source-enter link description here

The problem with SH is its view of Christ as inheriting divinity due to His life, rather than being born already Divine. It conflates the Spirit and Son.

It was evidently written during the second century by an influential person.

Evidence of this is that we have some early witnesses that ascribe the book to Hermas, the brother of Pope Pius I. The Muratorian Fragment attests to this: “Hermas wrote The Shepherd very recently, in our times, in the city of Rome, while bishop Pius, his brother, was occupying the chair of the church of the city of Rome.” If the Muratorian Fragment is accurate, we can date both the fragment itself and the Shepherd to the second century. -source-

As mentioned, SH promotes some false Christology.

The Shepherd does more than present to us a historical document that proves that penance as a means of absolving sin is not Apostolic–it shows us that the Bishops which succeeded the Apostles got a lot of things very wrong very fast.

The Shepherd makes the obvious error of being Binitarian at best, and Unitarian at worst. It conflates the Holy Spirit and Jesus Christ as a single being, an angelic being at that. The fact that a Roman Bishop’s brother wrote it and it was recognized as a plausible revelation shows that they did not have a firm understanding of the Trinity or Christology in general (which is inexcusable in light of what the Scripture clearly says and how earlier interpreters like Ignatius already wrote about the same topics). -ibid-

"That Holy Spirit which was created first of all, God placed in a body, in which it should dwell, in a chosen body, as it pleased him." This is Martini's translation. F. C. Conybeare renders the passage: "God made His Holy Spirit, which pre-existed and created all creation, to enter and dwell in the flesh which He approved." In this text the Holy Spirit appears to be a divine substance. But we must not suspect Patripassionism. The "flesh" is spoken of as a person who "walked as pleased God, because it was not polluted on earth." "God, therefore, took into counsel the Son and the angels in their glory, to the end that this flesh might furnish, as it were, a place of tabernacling (for the Spirit), and might not seem to have lost the reward of its service. For all flesh shall receive the reward which shall be found without stain or spot, and in it the Holy Spirit shall have its home." This passage appears to make the "tabernacling" of the Holy Spirit in Jesus a reward for the purity of his life. Jesus then becomes divine through the power of God, after consultation with the Son of God, who elsewhere in The Shepherd is identified with the Holy Spirit. -source-

So to answer the OP, did any Apostolic or Ante-Nicene Fathers believe that Jesus was a created being?, the answer would be yes, at that time the Shepard of Hermas taught something similar to the heresy that Christ was created.

There's a major problem searching literature for claims that some leaders of the early Church believed that Jesus was a created being, apart from wasting a massive amount of time looking for something that just isn't there. It is the problem of quoting out of context, and thereby giving a misleading impression. Some people have claimed that Justin Martyr said Jesus was created, and that Irenaeus did not believe Jesus to be uncreated God. I have read one book in particular that said:

“Justin Martyr, who died about 165 C.E., called the prehuman Jesus a created angel who is “other than the God who made all things.” He said that Jesus was inferior to God and “never did anything except what the Creator…willed him to do and say”

“Irenaeus, who died about 200 C.E., said that the prehuman Jesus had a separate existence from God and was inferior to him. He showed that Jesus is not equal to the “One true and only God,” who is “supreme over all, and besides whom there is no other.” (Should You Believe in the Trinity? p7, published W.T.B.T.S. 1989)

Well, let those early Church leaders put that to the test with their own writings:

Justin Martyr: “Christ [is] Lord, and God the Son of God,…appearing formerly in power as Man, and Angel, and in the glory of fire as at the bush….they call Him the Word, because He carries tidings from the Father to men: but maintain that this power is indivisible and inseparable from the Father, just as they say that the light of the sun on earth is indivisible and inseparable from the sun in the heavens; …and, for the sake of example, I took the case of fires kindled from a fire, which we see to be distinct from it, and yet that from which many can be kindled is by no means made less, but remains the same.” (Dialogue with Trypho, Chapter 128)

Irenaeus: “And this [text following] does declare the same truth: ‘Thy throne, O God; is for ever and ever; the sceptre of Thy kingdom is a right sceptre. Thou hast loved righteousness, and hated iniquity: therefore God, Thy God, hath anointed Thee.’ For the Spirit designates both [of them] by the name, of God – both Him who is anointed as Son, and Him who does anoint, that is, the Father. …Who is meant by God? He of whom He has said, "God shall come openly, our God, and shall not keep silence;’ that is, the Son, who came manifested to men who said, ‘I have openly appeared to those who seek Me not.’ …And again, when the Son speaks to Moses, He says, ‘I am come down to deliver this people.’ For it is He who descended and ascended for the salvation of men. Therefore God has been declared through the Son, who is in the Father, and has the Father in Himself – He who is, the Father bearing witness to the Son, and the Son announcing the Father... it is clearly proved that neither the prophets nor the apostles did ever name another God, or call [him] Lord, except the true and only God… not one of created and subject things, shall ever be compared to the Word of God, by whom all things were made, who is our Lord Jesus Christ. For that all things, whether Angels, or Archangels, or Thrones, or Dominions, were both established and created by Him who is God over all, through His Word, John has thus pointed out. For when he had spoken of the Word of God as having been in the Father, he added, ‘All things were made by Him, and without Him was not anything made.’ …But whatever things had a beginning, and are liable to dissolution, and are subject to and stand in need of Him who made them, must necessarily in all respects have a different term [applied to them], even by those who have but a moderate capacity for discerning such things; so that He indeed who made all things can alone, together with His Word, properly be termed God and Lord: ….they who were the preachers of the truth and the apostles of liberty termed no one else God, or named him Lord, except the only true God the Father, and His Word, who has the pre-eminence in all things….” (Against Heresies 3:6:1-2,4;8:1- 9:1;15:3)

“…the Word of God – who is the Saviour of all, and the ruler of heaven and earth, who is Jesus, as I have already pointed out, who did also take upon Him flesh, and was anointed by the Spirit from the Father – was made Jesus Christ… For inasmuch as the Word of God was man from the root of Jesse, and son of Abraham, in this respect did the Spirit of God rest upon Him, and anoint Him to preach the Gospel to the lowly. But inasmuch as He was God, He did not judge according to glory, nor reprove after the manner of speech.” (Against Heresies 3:9:3)

“…He received testimony from all that He was very man, and that He was very God, from the Father, from the Spirit, from angels, from the creation itself, from men, from apostate spirits and demons, from the enemy, and last of all, from death itself.” (Against Heresies 4:6:7)

“Now this is His Word, our Lord Jesus Christ, who in the last times was made a man among men, that He might join the end to the beginning, that is, man to God. Wherefore the prophets, receiving the prophetic gift from the same Word, announced His advent according to the flesh, by which the blending and communion of God and man took place according to the good pleasure of the Father, the Word of God foretelling from the beginning that God should be seen by men, and hold converse with them upon earth, should confer with them, and should be present with His own creation, saving it, and becoming capable of being perceived by it, and freeing us from the hands of all that hate us, that is, from every spirit of wickedness; and causing us to serve Him in holiness and righteousness all our days, in order that man, having embraced the Spirit of God, might pass into the glory of the Father….” (Against Heresies 4:20:4)

“The sacred books acknowledge with regard to Christ, that as He is the Son of man, so is the same Being not a [mere] man; and as He is flesh, so is He also spirit, and the Word of God, and God.” (Fragment 52)

“With regard to Christ, …the Man among men; Son in the Father; God in God; King to all eternity. (Fragment 53)

“Therefore, the Father is Lord and the Son is Lord, and the Father is God and the Son is God, since he who is born of God is God, and in this way, according to His being and power and essence, one God is demonstrated: but according to the economy of our salvation, there is both Father and Son….” (On the Apostolic Preaching 2:1:47)

“…the Son, as He is God, receives from the Father, that is, from God, the throne of the everlasting kingdom….” (On the Apostolic Preaching 2:1:47)

It has taken me over two hours to do this and if I had many more hours to spare, I could give the same treatment to more false claims about Tertullian, Hippolytus and Origen, claims that they believed the Son of God to be created, and therefore not God, when I have in front of me screeds of quotes that prove such claims to be false. But because those documents are so copious, and often so verbose, very few people will bother studying them carefully, to spot where less scrupulous people have just searched for misleading partial quotes to take out of context.

There were a few writers from that era who believed the Son of God, Jesus, to have been created (thus proving he could not be God) but none of them were Apostolic of ante-Nicene 'Fathers'. Arius, for example, was a third century presbyter, never "a church Father". "There exists a trinity [trias] in unequal glories", the Son as the first created being. (Quoted from Arius's poem "Thalia". See Rowan Williams. Arius, Heresy and Tradition, Grand Rapids: Eerdmans, 2002, 102)

The preponderance of literature of that era was overwhelmingly against the idea that Jesus was created, not because those 'Fathers' destroyed all writings to the contrary, but because the truth of the fully divine nature of an uncreated Christ was the foundation upon which the Church was built. That is why no Apostolic or ante-Nicene 'Fathers' ever wrote that the Son of God had a starting point in time, that he was created.