Do early Church Fathers support Catholic doctrine, as the Catholics claim? For example, St Ignatius writes: “Make no mistake, my brothers, if anyone joins a schismatic he will not inherit God’s Kingdom. If anyone walks in the way of heresy, he is out of sympathy with the Passion. Be careful, then, to observe a single Eucharist. For there is one flesh of our Lord, Jesus Christ, and one cup of his blood that makes us one, and one altar, just as there is one bishop along with the presbytery and the deacons, my fellow slaves. In that way whatever you do is in line with God’s will.” He was a disciple of John after all, and there are many more Fathers who write statements about the Eucharist and other sacraments.
Your question is hard to answer for a couple of reasons. First of all, what do you mean by “Catholic doctrine?” Do you mean Roman Catholic doctrine? The church itself is “catholic.” (which means universal). So, are you asking if the early church fathers support church doctrine, or do you mean to ask whether they support Roman Catholic doctrine? I am not sure. I will assume you mean Roman Catholic. Second, are you asking if someone like Ignatius supported the Roman Catholic Church? If that is your question then the question makes no sense, because there was no Roman Catholic Church when Ignatius wrote in the very beginning of the second century. He could not support an institution that did not exist. At that time the church in Rome was not preeminent among the churches and there was nothing even remotely like the Roman Catholic Church for Ignatius to support.
Or, thirdly, you might be asking whether what Ignatius wrote can be used now by the Roman Catholic Church to show that they are right (and by implication, other churches are wrong). My answer is that the Roman Catholic Church certainly does use Ignatius and others to support their positions, but in order to do so, they take Ignatius out of context. They try to pretend that he is speaking to the situation today (or 1000 years ago). This is an incorrect use of Ignatius. What he said should be applied to the situation in the early second century. Once it is applied to the specific situation, then we can as a corollary ask if it also, therefore, also supports things the Roman Catholic Church would say today.
So, let me do what we ought to do, which is to ask what Ignatius was saying in the quote above to the church of his day. In the early second century there were beginning to be a couple of heretical groups. There were not as many as there were later, but already by about AD 120 when Ignatius wrote, there were Gnostics (who deny the humanity of Jesus) and the Ebionites (who deny the deity of Christ). Ignatius is telling his contemporaries to not join in with such groups, as such heretics will not be saved. He tells us that only those in the mainstream of the church can partake in a true communion of the Lord’s Supper. He is telling us that the bishop (the head elder in a church at that time) and the other elders are the guardians of orthodox belief and that disciples ought to obey what they say. Does this support Roman Catholic claims? I say no. It supports Christian claims, but there is nothing there which supports Roman Catholicism in particular.
Sorry for a somewhat confusing answer to a question which could have more than one interpretation.