You can use discover method of our API. E.g. to get a list of English action movies sorted by popularity:

https://api.themoviedb.org/3/discover/movie?api_key=###&language=en-US&sort_by=popularity.desc&include_adult=false&include_video=false&page=1&with_genres=28&with_original_language=en

Notes:

1. Discover methods return only first 10 000 matches. If you need more movies, you must split your discover query into smaller batches, e.g. by years.
   
2. You can get the list of all valid genre ids by using genre API method.
   
3. "&with_genres=" parameter supports more genre ids being comma (,) or pipe (|) separated. Comma's are treated like an AND and query while pipe's are an OR.

Amazing! This is exactly what I was looking for. Thanks for your help!

I also want to send search word with genre just like you send in search api https://developers.themoviedb.org/3/search/search-movies E.g q="War" and with_genre=12

You can't limit search to specific genres, "&with_genres=" works only with TV and movie discover methods.

All I've seen is non-answers and highly-technical talk about "API" and things ordinary people don't know about.

@andricperez said:
All I've seen is non-answers and highly-technical talk about "API" and things ordinary people don't know about.

Making API Requests is usually done by code programmers, developing APPs and data query tools.
An API Request where there is a small typing error, a comma or space more or less, does not usually work.
But it is not an impossible subject to understand.
I, for one, don't program code.
I'm just a curious 71 year old.
Who for strange reasons decided to have fun with this subject.
If you found any non-answers and want some clarification, feel free to ask. :-)