The Orthodox Church mainly used the four Gospels we know since the second century.

Other writings are sometimes used as a second source, mostly considered «possibly reliable» .

Jerome had at least one gospel «that the Ebionites and the Nazarenes use and that we have recently translated from Hebrew to Greek and that is by most called the authentic Gospel of Matthew». The source seems to be an Aramaic version of the Gospel of Matthew, from which he points out some differences to the Greek text that remains his main source. There are also some passages cited that are really not contained in the Gospel of Matthew as we know it. It is most probable that more than one version of this Gospel existed. The terms «Nazarene Gospel» «Ebionite Gospel» and «Hebrew Gospel» are used by several authors (Hegesipos, Eusebios, Epiphanios). It seems that there were different editions but it is not evident to which extent and which edition is actually cited. This topic is broadly explained in Wikipedia.

Clemens of Alexandria also quotes a Gospel of the Hebrews, which he quotes like a possibly valid source; however we now found the cited passage in the Gospel of Thomas, logion 2. It is thus possible that Clemens had in fact used an Aramaic version of the Gospel of Thomas. It is thus possible that Clemens of Alexandria counted the Gospel of Thomas among the possibly valid sources.

Finally, the passage introduced into the Gospel of John (8:1-11) in a late state, must have been taken from a source that is unknown today.

Variants of childhood gospels were long time used in the Orthodox Church but not a basis of belief.

The largest number of «gospels» were only used in the Gnostic branch of the church and clearly refused in the Orthodox Church.

Unfortunately we don't have a particularly great documentary record when it comes to non-canonical books. That said, there is some clear evidence that at least some people in the early church accepted other "gospels" as Scripture.

Gospel of the Hebrews

Let's first turn to early church historian Eusebius. He divides the existing books into three groups: widely recognized, disputed, and heretical. (Histories, 3.25) His "widely recognized" canon largely agrees with our own, but the "disputed" category is worth noting. These are works that he didn't simply dismiss, but suggests that at least some in the church accepted them. In this list, one in particular can rightly be called a gospel – the Gospel of the Hebrews.

According to the Eerdmans Dictionary of the Bible, among those who knew and used the book are Clement of Alexandria, Origen, Didymus the Blind, Cyril of Jeruslaem and Jerome. And Klijn, "Jewish-Christian Gospel Tradition," argues that Hegesippus accepted it, based on Eusebius's mention of him (Histories, 4.22).

The Gospel of Truth

Perhaps even clearer evidence for the existence of someone holding to more than four gospels in the earliest centuries is found in the writings of Irenaeus. He attacks a prominent gnostic, Valentinus, over the matter:

But those who are from Valentinus, being, on the other hand, altogether reckless, while they put forth their own compositions, boast that they possess more Gospels than there really are. Indeed, they have arrived at such a pitch of audacity, as to entitle their comparatively recent writing “the Gospel of Truth,” though it agrees in nothing with the Gospels of the Apostles, so that they have really no Gospel which is not full of blasphemy. (Against Heresies, 3.11)

Others

Eusebius specifically mentions several more "gospels" in his "heretical" category – the gospels of Peter, Matthias, and Thomas. These and others like them don't have much explicit evidence for their acceptance by some in the church, though presumably Eusebius wouldn't have even mentioned them if no one accepted them. And indeed, their relative prominence is used as evidence for acceptance: see, for example, What is the basis for saying that the Gospel of Thomas was accepted as scripture by early Christians?

Summary

So yes, there were people who associated themselves with Christianity – some typically considered "orthodox," some not – who seem to have accepted more than four gospels. Two of the best documented "fifth gospels" are the Gospel of the Hebrews and the Gospel of Truth.