What is the legitimate Islamic solution for a woman who was subjected to sexual intercourse under dubious circumstances, and two men dispute the paternity of her child, with each of them clinging to his marriage to her?

If two men have intercourse with a woman due to a misconception (shubhah), and she gives birth to a child who could be from either of them, and then they dispute over him, the child is presented to the Qafah (trackers/physiognomists) along with them. He is then affiliated with the one to whom the Qafah attribute him. In the current era, DNA fingerprinting takes the place of the Qafah in determining the child's lineage in such cases. The Islamic Fiqh Academy has permitted reliance on DNA fingerprinting to establish lineage in cases of disputed paternity for those of unknown lineage, or in cases of shared intercourse due to misconception. Matters of dispute and lawsuits are decided by the judiciary.