As the case against Rex A. Heuermann grinds toward a trial, his lawyers have vehemently sought to exclude damning DNA evidence central to his prosecution in the Gilgo Beach serial killings. But on Tuesday, the judge presiding over the case in Suffolk County, N.Y., admitted the genetic findings that prosecutors say connect Mr. Heuermann to seven murdered women found along an oceanfront parkway on Long Island more than a decade ago. The judge, Timothy P. Mazzei, also declined the defense’s request to sever the case into separate trials for some of the killings. The rulings cut off two major offramps for Mr. Heuermann as the case, which has transfixed the public and set off a wave of true-crime shows and podcasts, moves forward. A trial is expected next year.