Sukue - I've just read your post and had to respond. I'm guessing you're pretty young which probably means I'm old enough to be your mother :)
The father of your child is bullying you! He's a bully! What he is doing to you is domestic abuse. I don't know if you realise but abuse doesn't have to be physical, he doesn't have to hit you, it can also be mental, deliberately saying really hurtful things to you, degrading you, calling you his prostitute is degrading you! He knows exactly what he is doing and his actions are deliberate. When he said you have too much pride he meant you're being too strong, he wants you to be weak because then he can bully you and take control of you and your emotions. He is a very toxic man and you may not realise it at the moment but the best place you can be is no longer in a relationship with him.
His actions do not show he wants to be part of his daughter's life. If he wanted to be part of his daughter's life he would ask to see her, he would want to take care of her, buy her what she needs etc, he wouldn't need you to beg him, and that is what you're doing. All the time you beg him he feels in control and will continue to abuse you.
Perhaps in time he will grow in to a better person and a better dad but at the moment you are better off without him. STOP allowing him to abuse you in this way, BE STRONG, DON'T beg him or apologise you have done nothing wrong. It is not your fault her dad is failing in his responsibilities. STOP contacting him as he sees this as weakness and you as needy which gives him strength to abuse you.
Do you have people around you can talk to and who can support you? You have two things to deal with here, one is access and the other is financial support, he should be supporting his daughter financially.