I heard that we do not use the word 'want' after the word 'will' because will includes the meaning 'wish'. But I saw lots of people using the expression like no one will want to marry me.
Yes it's perfectly correct. Here's some sentences you could use it in:
No one will want to marry me.
After being alone for so long, I will want to go home.
We will want to rest after the long hike.
Whoever told you this didn't have a great argument. Sure, the word "will" can mean "wish", (although this is a rare usage) but lots of words have multiple meanings. Just because one of them might be wrong doesn't mean they all are.