When the Christianity was in its nascent stages, Buddhism was a major religion in the Areas of Bactria, India and Central Asia. Given the cultural and trade contacts between the Levant( where Christianity was founded) and these predominantly Buddhist areas it seems highly likely that Buddhist teachings and doctrines would have influenced Christianity. If so to what degree did they influence???
It's a little difficult for me to cite sources for this answer, because the answer is that there is no evidence of Buddhism influencing early Christianity. I suppose I could gather up some of the secondary sources that back this claim.
Consider the reasons for this:
Some later Christian authors show an awareness of Buddhism (Clement, Hippolytus, e.g.), but little in the way of sophisticated knowledge of Buddhism. They merely have heard of it as a religion among the Indians.