Is it permissible to fast on my birthday once a week, emulating the Prophet, peace and blessings be upon him, who used to fast on Mondays?

It is not permissible to single out Sunday for fasting because one was born on it. The Prophet, peace and blessings be upon him, fasted on Mondays because it was the day he was born, the day revelation descended upon him, the day deeds are presented to Allah, and a day of forgiveness for sins. The Prophet's saying, "That is the day I was born," does not mean fasting on one's birthday, but rather an explanation of the greatness of the day he was born. If fasting on one's birthday were legislated, the Prophet, peace and blessings be upon him, would have clarified it, and the Companions would have done it.