Spellthief instead of Dorans Ring on AP mid?

No because it has a really long cool down of not receiving gold on hit after you kill a minion

It's a very greedy starting item. You don't get the better sustain nor the health. You can easily be punished for it. It is similar to buying but for AP mages. You can get more gold out of it but it will not be easy as you are at a disadvantage in AP, HP and sustain. I would probably entertain buying it as a second item if you got FB and felt confident you could continue to win lane. I would not get as a first item in mid though. Doran Ring just adds too many stats to compete with at level 1.

actually it is worth ish. the passive it gives is like an extra 15 true damage when fully stacked... so if you're roaming and find a fight early on that actually helps alot. it also pays for itself, and if its treated like your dorans item its the last item to go so can't go wrong with it. ill give an example... ezreal. you get this item on him mid, and you get to level 2. q, e, auto. the ratios on most abilities is actually less damage with the dorans ring compared to the passive of level 1 spell thief. remember though, dont bother upgrading it if its your start buy and you're not support.

it used to be usable on ap trist, but really why would you? It gimps you and the gold doesn't add up that highly.

It could work, because you get money from poking and cs; while you get mana regen and ap.

But Doran gives you more ap, and hp... so it's hard to say.