Hi thanks for your question.
You had your periods on december 13th and spilt from your partener on December 19th.
Your partener is not father of your baby ,since you had your periods on December 13th,so you were not pregnant before that.You got seperated from your partener on december 19th.
You cannot get pregnant from sexual acts that took place between December 13th and December 19th ,as this was your safe periods.
So most probably the other man with whom you slept is father of your child.
Finally DNA finger prints is confirmatory test.
Hope this answers your question.

Hello,
To tell you the truth, it will be very difficult to place the parternity of your child in any of those two partners with just the presentation you gave, given that there are many factors that are involved.
Taking a detailed look at the situation can help us determine the most probable father for your child but the best test for parternity is DNA cross matching or you can begin the most simpler ones knowing the blood group + rhesus for each of your fathers including yours and cross checking with that of your baby. With the dates provided, it difficult to deduce. 1stly, you had sex with your first partner after your period on the 13th December till the 19th which is about 6 days after last menstrual period. Then you had sex again on 13th January and only found out on 19th Feb that you were pregnant and it was 6 weeks ( would have known if it was ultrasound estimation or calculated using gravidometer). My estimate from the 13th Dec of last period till 19th Feb gives 9 weeks 1 day amenorrhea and about 7weeks pregnant if ultrasound measurements. The other calculation involving the 2nd man you had sex with on 13th January gives 4wks 6 days pregnancy post intercourse (i don't know if you had your period a week or so before you had sex with the 2nd partner or not).
-Do you usually have regular periods? If not then it makes it difficult.
-Do you know if any of the men have fertility issues i.e like having difficulty to conceive? If you do not know then it will be difficult.
Conclusively it would not be easy to determine who the father of the baby is just by the information you provided given that both parents have almost equal chances of getting you pregnant. If the 13th December was your last menstrual bleeding, then it is possible that the 1st partner is the father.
Like i said, if you have access to DNA cross matching, i'll suggest you get that done.

Hope this helps