The possessive が is literary and archaic, and I don't think it's productive anymore. You'll rarely see it outside several fixed expressions such as: [我]{わ}がＸ (e.g. 我が[家]{や}、我が子、我が国、我が道、我が命、我が物(にする)、我が物顔(で)...), [我]{われ}ら (我らが母校、我らが祖国、我らがヒーロー)、『君が代』... (Not 私がＸ or 私たちがＸ, since the が is literary but 私・私たち are not.)
- [我]{わ}がＸ (e.g. 我が[家]{や}、我が子、我が国、我が道、我が命、我が物(にする)、我が物顔(で)...)
- [我]{われ}らがX (e.g. 我らが母校、我らが祖国、我らがヒーロー)
(Not 私がＸ or 私たちがＸ, since the が is literary but 私・私たち are not.) - 『君が代』
- Xがために (=Xのために) (e.g. [誰]{た}がために、これがために、～せんがために)
- Xが如く (=Xの如く)