Jesus was born during the reign of Augustus. Though we don't know what the coin was that Jesus was given there is good argument that it was this one. Gospel of Mark chapter 12:
14 They came to him and said, “Teacher, we know that you are a man of integrity. You aren’t swayed by others, because you pay no attention to who they are; but you teach the way of God in accordance with the truth. Is it right to pay the imperial tax[b] to Caesar or not? 15 Should we pay or shouldn’t we?”
But Jesus knew their hypocrisy. “Why are you trying to trap me?” he asked. “Bring me a denarius and let me look at it.”16 They brought the coin, and he asked them, “Whose image is this? And whose inscription?”
“Caesar’s,” they replied.
17 Then Jesus said to them, “Give back to Caesar what is Caesar’s and to God what is God’s.”
Collection : Through History Graded Coins