13 weeks-Blood Only. There is a new option available which uses the small amount of fetal dna present in mom's blood. Unlike other methods, there is no direct sampling of fetal blood/tissue. It requires a cheek swab from dad, but it does require 10 tubes from you. It uses PCR technology to amplify the dna.
10-18. Paternity testing requires genetic material from the baby. The soonest it can be obtained relatively safely is 10wks by cvs or 15wks by amniocentesis. Both these procedures have significant risks to the pregnancy. The safest option, when possible, is to wait until the baby is born to perform paternity testing. You will also need blood from the mom and the suspected dad to perform the test.
After bith. Paternity testing requires dna testing on a blood test from mom and dad but requires a comparison with the dna of the baby. To reliably get dna material from the baby, before birth, would require an invasive test such as chorionic villi sample (by 12 weeeks) or amniocentesis (by 16 weeks). Both tests carry a significant risk to the pregnancy.