Hi,
Welcome to the ehealthforum and I am glad to help you out. Since your last menstrual period was on 16th july, so your ovulation would have been around 29th July. Pregnancy occurs during the time of ovulation. Ovulation is the release of a single, mature egg from a follicle that developed in the ovary. It usually occurs regularly, around day 14 of a 28-day menstrual cycle.
So you could have conceived around 29th july if your earlier cycles are regular. However, this may not be 100% true and the real answer can come only from the paternity test. I sincerely hope this information helps. Take care.