Answer
Based on official Jordanian legal texts
The Jordanian Personal Status Law No. 15 of 2019 sets the custodian's conditions in Article 171: the custodian must be of full age, sound mind, trustworthy, and capable of raising, protecting, and safeguarding the child in faith, character, and health; free of serious contagious disease; not previously convicted of a crime against morals; and not an apostate.
Article 171 adds two specific conditions: a female custodian must not be married to a man who is a stranger (non-maḥram) to the child, and where the custodian and child are of different sex the custodian must be a maḥram relative — both to protect the child and serve his interest. These conditions are assessed at the time custody is considered, not only at the moment of ruling.
These conditions connect to the order of custodians in Article 170, which makes the biological mother the most entitled, then those after her; if a condition in Article 171 fails for the person whose turn it is, the right passes to the next. Article 172 provides that the right of custody lapses if any condition fails.
The governing standard throughout is the child's best interest, and assessing whether the conditions are met remains within the Sharia Court's competence on the facts of each case.
This is a general explanation based on Jordanian Personal Status Law and does not replace advice from a qualified lawyer in a specific dispute.