First Holy Communion is usually the first celebration of the Holy Eucharist. Because baptised children from these ecclesial communities normally received First Communion along with Baptism and Confirmation, these children do not usually celebrate First Holy Communion again. Orthodox children are usually not presented for First Communion even if they are enrolled in Catholic schools.
Speak to your pastor about your particular situation, especially if the child has a Roman Catholic parent or if the parents would like to be received into the Catholic Church.
[1] Lumen Gentium, 11.
[2] Gravissimum Educationis, 3
[3] Lumen Fidei, 43.
[4] Familiaris Consortio, 52; cf. Evangelii Nuntiandi, 71.
[5] For common examples, see the Archdiocesan resource Invited to the Feast, especially pp. 21-22.