DNA testing on deceased father ? Definitely. There are a number of options available in such cases where the alleged father has passed away. However, we might begin by saying that the most reliable and conclusive DNA test is the DNA paternity test which would mean having DNA samples from the alleged father and child/children and using these for laboratory analysis.
If the dad has just passed away and not buried you may consult a pathologist to collect forensic DNA samples, typically nails or hairs can be used. Hairs would need to have the root or follicle and thus, they would need to be plucked out. Usually around 4-6 hairs will suffice.
If the father has been buried things become harder. However, you can still do a DNA testing on deceased father even if the corpse is buried. You need to get permission for an exhumation but once you have done this, a forensic doctor can take the necessary bone samples from the corpse of the alleged father and send these for testing. Typically, 2 grams of bone are used taken either from the humus or femur. Teeth can also be used assuming he does not have dentures.
If the father has been buried, you could also consider whether you may have any DNA samples such as a hair brush or toothbrush belonging to the deceased; since getting an exhumation is so costly and tedious, this is definitely worth considering.
Another option for DNA testing if the father is dead is doing an avuncular test; for example a test with the alleged father’s brother or sister; a grandparents test or a DNA sibling test. These tests will never give as high a probability as a paternity test with the father’s samples but can still, nevertheless, give you a conclusive answer.
DNA testing if the father is deceased can thus be done and there are many options available.