the female of certain animals, to bring forth young (of animals)
牸 centers on the female of certain animals, especially domesticated ones, and by extension the act of bringing forth young.
牸 combines 牜 (cow) with 字, which likely contributes the sound and the idea of breeding or offspring, together expressing a female animal that bears young.
The cow radical 牜 on the left and 字 (character/letter) on the right can be remembered as a female cow marked with a special character to indicate she is a breeding female.
For シ, imagine a female sheep (シ sounds like 'she' in 'sheep') giving birth: she -> シ, and the cow radical reminds you it's about female animals.