Welcome @Ayyan !!
Searching the site for simpler terms like “add field to search” will yield results where others have solved the problem already.
This came up with a quick search using those terms
Add some field on a search box - Epicor ERP 10 - Epicor User Help Forum
Also, generally speaking, the default search dialogs are not customizable in Classic UI. They might be in Kinetic, but I don’t know. That is why Epicor gave us Quick/BAQ searches for this purpose.
@MikeGross
Thanks