is his name on your birth certificate?
is your last name his or your mothers?
have you asked your mum other family members for any information they know?

even if you just have his name, where he lived and a rough idea of his age you can try births deaths and marrages, or just google it and see what comes up.

was your mum married to him? there will be some sort of record or this.

start with these and see what you can find out from this.

good luck i hope you find what your looking for