Single and nearly 16 weeks pregnant

Right... I had a boyfriend of about 4 months on and off and hes finally ended it with me for no reason exsept he says he feels unwanted all because i feel ill most of the time and i just need space until i feel better with the pregnancy and he said he understood that but obviously not.. there is alot more to it but im cutting it short really.. this baby could either be my ex befores (jayys) or it could be the recent ex (tims) it wasnt planned obviously and it was a mistake with (jayy) used protection but it split and i didnt know till he told me months after but my recent ex (tim) knows all this that it might not be his and to be honest he couldnt give a crap he was nervous at start and his parents wanted me to have an abortion but i cant do that as iv already had a misscarriage and that broke me to pieces.. and now (tim) has basically ruined my life proper turned on me and turned violent and hes forever drunk but he as always drank alot so i cant tell him not to.. so he doesnt want anything to do with this baby and told me to drop dead.. but my ex (jayy) said he would be there if its his and give us another try cause were really close still .. so got to have a dna when babys born obviously and go from there..

But anyways i was wondering on the birth certificate if the father is (tim) do i have to put him on it? as he doesnt want anything to do with me or the baby (people may think its wrong but its my decision i just want to know what happens and if you can leave it blank or not) but if its (jayys) then he will go on it as he wants contact and everything.

Any advice would be good about it if youve been through it especially and know what happens x