Some OT passages:
(The plagues)
Exodus 7:5 And the Egyptians shall know that I am the LORD, when I stretch forth My hand upon Egypt and bring out the people of Israel from among them.
Exodus 7:17 Thus says the LORD, "By this you shall know that I am the LORD: behold, I will strike the water that is in the Nile with the rod that is in my hand, and it shall be turned to blood,… (Also see Exodus 8:10; 8:22; 9:14-16; 9;29; 10:2)
Exodus 19:9 And the LORD said to Moses, “Lo, I am coming to you in a thick cloud, that the people may hear when I speak with you, and may also believe you for ever.”
Deut. 4:33-35 Did any people ever hear the voice of a god speaking out of the midst of the fire, as you have heard, and still live? Or has any god ever attempted to go and take a nation for himself…by signs, by wonders, …according to all that the LORD your God did for you in Egypt before your eyes? To you it was shown, that you might know that the LORD is God; there is no other besides Him.
NT: (This passage does not refer to a specific miracle, but is a statement by Jesus that His miracles/works should serve to lead people to believe in Him.
John 10:37-38 If I am not doing the works of my Father, then do not believe me; but if I do them, even though you do not believe me, believe the works, that you may know and understand that the Father is in me and I am in the Father."