Is it permissible to perform a DNA test to prove the lineage of a family that claims a connection to the third grandfather but refuses to prove it with documents?

If your family's lineage to your ancestor has been well-known and established for a long time without objection, then it is not permissible to challenge or deny it using genetic fingerprinting. However, if the lineage is recent and without proof, then the lineage is not established. The rule "People are trustworthy concerning their lineages" means accepting a lineage from which no benefit is derived or blame averted, and it does not mean believing a claimant of lineage without evidence. Furthermore, challenging lineages without legitimate, Shariah-compliant evidence is not permissible, and if a lineage entails a legal (Shariah) consequence, then it must be proven. The general principle is that people are trustworthy concerning their lineages, except for those who claim nobility or lineage to individuals of high standing; their claim is not accepted merely, but rather with proof through a family tree, the testimony of upright witnesses, or the testimony of common knowledge. If the lineage of this family is not proven by widespread fame, documents, or the testimony of upright witnesses, then there is no harm in requesting proof from them. If the dispute persists and there is no way to resolve it except through genetic fingerprinting, then there is no harm in that.