Did any of the Church Fathers think the current-day Gospels were not inspired?

Lists of the names of the Church Fathers vary. But in any case they show an evolving attitude toward the Gospels as inspired scripture. In the earliest church the only "scriptures" were the Jewish ones. In the gospels, when Jesus quotes from scripture he quotes of the "Old" Testament, and Paul does likewise in his letters.

Among the Church Fathers, Justin Martyr (c/ 150 c.e.) is the first to talk about what we call the gospels per se. Earlier, Ignatius of Antioch and Polycarp quote from them but did not speak about them as such. Justin refers to them as "memoirs of the apostles." He doesn't say that they were inspired, but he does not deny the idea either. He uses the "memoirs" term several times without naming them. He speaks of them as authoritative sources of church tradition along with Old Testament writings, and they are to be read in worship services. Here is an example.

on the day called Sunday, all who live in cities or in the country gather together to one place, and the memoirs of the apostles or the writings of the prophets are read, as long as time permits; then, when the reader has ceased, the presider verbally instructs, and exhorts to the imitation of these good things. Then we all rise together and pray, and, as we before said, when our prayer is ended, bread and wine and water are brought, and the presider in like manner offers prayers and thanksgivings, according to his ability, and the people assent, saying Amen... (First Apology 67)

Debates about which gospels were truly inspired heated up as a result of the Roman church leader Marcion of Sinope accepting only the Gospel of Luke and denying the inspiration of the Old Testament writings. He also denounced the God of the Jews, arguing that such a jealous, vengeful deity could not be the loving Father described by Jesus. These teachings resulted in his excommunication. The orthodox church reacted to the challenge of his movement, as well as the proliferation of Gnostic literature, by affirming the authority of the OT and rallying around the four gospels, and no more than four.

Tatian composed his Diatessaron around 170 C.E. It is now lost but seems to have been what we today would call a harmony of the gospels, attempting to combine all four into one. It may be argued that because he saw a need to create one gospel from the four, he did not consider them to be "inspired" in the sense that Christians use the word to day; but he is sometimes counted among the Apologists but has also been criticized for espousing the heresy of Encratism.

Irenaeus of Lyon c. 185 clearly affirmed the four gospels as inspired, and only four. In his key work, Adversus Haereses Irenaeus denounced groups that used only one gospel. He declared that the four gospels are the "four pillars" of the Church.

It is not possible that there can be either more or fewer than four, [because] there are four zones of the world in which we live, and four principal winds, while the Church is scattered throughout all the world. (III.11.8)

Irenaeus marks the emerging of the proto-orthodox consensus on the inspiration of the gospels. By the end of the second century all four gospels--no more and no less--were accepted, and all four were considered inspired.

Not to define exactly what is a Christian, but, very broadly speaking, there were early Christians who rejected parts of what today's Christians consider to be the New Testament. But, by doing so and thus having a presumably different faith, they are not widely considered "Church Fathers".

https://en.wikipedia.org/wiki/Church_Fathers

Yet, as heretics so-called, Origen and Tertullian are considered by some to be "Church Fathers".

So, the quick answer to the OP question is it depends on your definition.

As to the others at that time, Marcion of Sinope is one example of an early "Christian" who rejected the Gospels of Matthew and John.

http://www.ccel.org/ccel/schaff/anf03.v.iv.v.v.html

The primary problem wasn't particularly rejecting books of the New Testament, but rather interpreting the books in a new and different fashion. This problem, obviously, continues to the present day.

http://www.ccel.org/ccel/schaff/anf03.v.iii.xxxvii.html

So, yes, depending on your definition of "Christian" and "Church Father", a case may be made that yes certain books were rejected by them as inspired.