Many hymnals and religious works that I was taught from often used the expression 'Jesu's'.
When referring to myself personally, I much prefer 'Douglas's'.
The Latin noun Iesus is irregular, and has a unique declension whereby both the genitive and vocative forms are Iesu. German and apparently Danish also use Jesu as the genitive, and German also used the Latin accusative form Jesum until fairly recently. (Possibly still used in Catholic schools, but no longer in general conversation.)
This is why a handful of hymns whose English lyrics are translations from Latin (O come all ye faithful) or German (Jesu joy of man's desiring) use Jesu rather than Jesus.
If you were referring to the central character in one of these hymns then I suppose you might use Jesu's, but otherwise Jesus' is conventional. Jesus's is in no way "wrong" and some secular writers prefer it.