The precise birth date of Apollonius of Tyana is unknown. The birth date of Jesus Christ is also unknown, but sometimes asserted and speculated upon. However, it is generally thought that the two lived around the same time. The most common estimates for his birth put it around 15 CE and his death around 100 CE, though some quote his lifespan as "more than 100 years," which would make those dates inaccurate. Another kink in the estimate is that some say he was older than Jesus Christ. The above dates would make him slightly younger than the commonly cited date of Jesus Christ's birth. Since there are no contemporary sources for either of their births, there is no way of knowing which, if any, of these estimates are correct. We can say that if Apollonius of Tyana lived, he did so in the first century. If Jesus also lived, he did so in the same century as Apollonius of Tyana.
Apollonius of Tyana is credited with similar qualities as Jesus Christ. They both are said to have ascended to Heaven. There are stories of both performing miracles. They were both spiritual teachers. However, they did not have identical beliefs. Jesus taught his followers that God answers prayers. Apollonius of Tyana believed in a god who was pure intellect and taught his followers that the only way to converse with God was through intellect. He taught that prayers and sacrifice were useless and that God really did not want to converse with men. In this way, they would have been in competition with each other if they preached in the same areas. Some say that they were and that they did.
Apollonius of Tyana's name stems from where he was born -- Tyana in Cappadocia. That is in modern-day Turkey. It is said that he also traveled to Greece and Syria. Jesus traveled in the Middle East as well. There are also claims that he went to India during the years of his life for which the Bible does not account. Therefore, there is a chance that the two did cross paths and compete with one another for followers. However, the similarities could also be explained by crossover stories. Furthermore, there is absolutely no mention of Apollonius of Tyana in the stories of Jesus and there is no mention of Jesus in the stories of Apollonius. Apart from speculation, there is no reason to believe the two ever met, if they existed.
When it comes to the miracles of Apollonius of Tyana, the veracity of those claims falls to personal beliefs. It is said that he saw a vision of the death of Emperor Domitian as it occurred. He reportedly cleansed a boy of demons or a demon. Some stories of his demise, which is also quite a mystery, say that he disappeared while on trial for "magic" and ascended into Heaven. These stories cannot be proven. If Apollonius were found to have not existed, it would be easy to say these miracles did not happen. Otherwise, it is a personal choice to believe them or not to believe them.
The most pressing question, which is that of his existence, is actually the least complicated mystery concerning Apollonius of Tyana. The most extensive and earliest lengthy biography on the man is a work by Philostratus written in 225 CE. That does nothing to prove his existence. There is no way to say whether the sources Philostratus cites truly existed or whether he was making it up. He certainly never met the man. Nonetheless, there are numerous letters and pieces of work by Apollonius of Tyana that exist to this day. In this way, Apollonius is more provable than Jesus Christ. Many of the proposed documents are likely to be frauds. However, at least one in particular -- an excerpt of his "On Sacrifices" -- is regarded as genuine, as in a piece written by Apollonius of Tyana himself. It is by no means absolutely certain that Apollonius of Tyana lived. Nonetheless, it is easier to entertain than stories of other miracle workers that appeared in history hundreds of years after their deaths and who left behind no contemporary writings.