Can a Muslim claim to perform miracles by praying for Muslims for healing?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Anybody who happens to have some miraculous thing (Karamah), should conceal it and should not boast because of that happening as doing so is contrary to the essence of Karamah. Allah Says (what means): {So do not claim yourselves to be pure; He is most knowing of who fears Him.} [Quran 53: 32]

No doubt that there are some people that have their Du'aa’ (supplications) to cure some sick person answered.

In fact, there are among the servants of Allah, some whose queries are answered by Allah for the sincerity, frankness and faithfulness that Allah Knows in them.

Allah knows best.