You can only exchange ones you've summoned, have, or are limited that you can't get anymore. Otherwise the exchange doesn't show up. IE: I can't exchange my Quintus fragments.

SS since you mentioned Searsha. You don't get an exchange for it.

i

Right but its giving me the option to exchange my fragments for Taya and Searsha. Searsha has a very limited number to get from the Plarium Points and Taya I'm getting from DT Rewards. I'm glad Quintus isn't on the list but Searsha is, so is Yannica.

EDIT: Ok so it blocks you from Searsha but she still shows up. That's good at least. But I'm still wondering for the Clan Coin Champs and DT Champs

Post a screenshot of it showing you can exchange Searsha. Posted my F2P account's fragments above and it doesn't have the exchange on Searsha.

My Yannica doesn't have an exchange. 

i

My DT champs don't have exchange

i

My Zinogre does, but that might be because she can be summoned from the pool or because is limited time only? Who knows. Only one on my list that I have at 100/100 that I can exchange that I don't have summoned yet.

All your fragments will always be in the Fragment Summon list. It isn't a Maud only list of champs.

i

Look for this symbol in the top right corner. Those are the only ones you can exchange in your list.

i