Ancient Fruit grows in any season other than winter, though they take almost a month to grow to maturity even with growth-accelerating fertilizer. So, they're best planted in the spring to ensure harvests throughout summer and fall. Aside from that, you can grow just about anything year-round in the greenhouse, once you unlock it. Space in there is limited, though.
Check out the Crops page on the wiki. it will give you everything you need to know. https://stardewvalleywiki.com/Crops As important as what seasons a crop grows in is how many harvests you can get from one planting. Most crops, you plant a seed, it grows, you harvest it, then you have to replant. But some continue to grow and give you multiple harvests on one planting. Green beans, hops, peppers, eggplant are a few examples, as is ancient fruit references above. And corn not only gives you multiple harvests, it grows across two seasons. It's not that much of a moneymaker, but it's very handy for stockpiling food. (I harvested over 800 corns from one planting in one field over two seasons and made them into tortillas. I'm still eating them five game years later.) Fruit trees only grow in one season, but if you plant them around the border of the greenhouse, they grow all year, even winter.
There are a few overlap crops that can be grown in multiple seasons. -Coffee beans can grow in the spring and summer. -Wheat can be grown in summer and fall -corn can be grown in summer and fall -Ancient fruit grows during all seasons but winter.
Oddly enough, the world's food problems is more about (uneven) distribution than production. Like in SDV really /takes off job hat. Pretty sure the OP got this link earlier, so maybe you should check it out? Faster than posting on a forum and waiting for an answer. https://stardewvalleywiki.com/Crops When looking for info on crops, I prefer to check out the season's page instead though. Better overview there. https://stardewvalleywiki.com/Spring#Crops (and so forth)
