fosterage

Indeed, I repent me of what was done by me to her, for that, in any case, she is my nurse and hath over me the right of fosterage.

From The Book of the Thousand Nights and a Night — Volume 07 by Sir Richard Francis Burton

The terms of fosterage seem to vary in different islands. 

From Journey to the Western Islands of Scotland by Samuel Johnson

A child in fosterage was reared and educated suitably for the position it was destined to fill in life.

From Encyclopaedia Britannica, 11th Edition, Volume 4, Slice 4 "Bradford, William" to "Brequigny, Louis" by Various

When Mardas saw Gharib his reason fled, and he said to him, "O my son, I am under thy protection: so deliver me in right of my fosterage of thee!"

From The Book of the Thousand Nights and a Night — Volume 06 by Sir Richard Francis Burton

This conjecture is corroborated by the numerous instances in history and in story of fosterage affection proving, when tested, stronger than the natural affection of relatives by birth.

From The Glories of Ireland by P. J. Lennox