If you are talking about APIs to deal with photoshop, there are some companies on the market that have products ready-made to do so, but here I cant't promote them.
You can even have a server with photoshop, and use these APIs from these companies.
Generally these companies developed themselves from markets like press/media/broadcasting contents.
If you want to do it just for yourself as a single user, I do not know cheap products for that.
Thanks, I just learn how to do.
You definitely can, provided that you build an HTML Panel that hosts your website, and the clicks are made within it.