Yes; however, establishing paternity is a civilian matter and thus state laws where the father is domiciled are most likely to apply.
As a practical matter, the father’s commander can make the process easy or difficult depending upon their level of cooperation. In general, the commander’s role is to advise the member of the paternity claim and refer him to counsel; assist a member if he acknowledges paternity; and to respond to the complainant. The commander does not have authority to order a blood sample or to enforce compliance with a court order to submit a sample; however, it is possible to have voluntary samples drawn by military health officials, but the degree of cooperation varies from location to location.
Once paternity has been established, the children are entitled to military health care and insurance (TRICARE). A military ID card is required to prove eligibility. If the member will not cooperate in getting a card for the child, his or her commander can coordinate issuance of the card.