These seeds are unique rewards after completing some challenges:

ATENTION:
Always spare some crops to put in the seed maker because the seeds will not be sold!

Ancient Flower: Mail from Gunther after shipping 5 ancient fruits
Ancient Tuber: Mail from Gunther after shipping 5 ancient flowers
Ancient Nut: Ship 5 Ancient Tubers and complete CC/Joja - Mail from Morris or from Junimos
Ancient Fern: Get 10 hearts with all Vanilla non-marriable NPCs and Ship 5 ancient nut
Ancient Coffee Bean: Complete Qi challenge (get to level 25 in skull cave), ship 5 Ancient Fern and you will get a new challenge from him (obtain level 10 in all skills - if you're using level extender it should work up to level 20)
Ancient Olive - Ship one ancient coffee (obtainable through a keg)

Fiona's Prize - Ship 5 ancient olive then you will obtain Fiona's prize which grants you a Stardrop!

Artisan Goods you can make with the crops:
Ancient Nut Milk - Oil Maker
Ancient Coffee - Keg
Ancient Olive Oil - Oil Maker
Ancient Flower Honey - Bee House
Ancient Nut Butter - Butter Churn (Artisan Valley)