I am currently pregnant and me and the child's father have broken up, which he doesn't like, so he is threatening to fight for sole custody when the baby is born. I do not use drugs or drink I am currently un-employed and he is not, does he have a better chance of getting this child, even though I've done nothing wrong?

No, to get full legal and phsycial custody he would have to prove you an unfit mother,

He may get joint custody. But to be honest, expect this just to be threats normally, he is trying to use the future child to control you.

I noted you were going to get an abortoin in your other post??

But you need to stop contact with him, if he is threatening you and worry about you and baby, once the baby is born, you file for custody and child support, if he wants some custody or visits he will have to file for that