Hi,

You can inherit the search view of the corresponding model for this. if you take the example for the model res.partner, if you need to search the search bar based on the website field of the partners.

First, activate the developer mode, then if you click in the laddy debugger button near the logged in user name, you can see an option Edit Search View,

Then,

In the pop up you are getting add the bit of code to search the website field too,

For doing the same from the code, please have a look at this link to see how to inherit the search view: Adding filters to existing search views

Thanks