Hello Himanshu, 

Kindly clarify that where you want to show the product drop down inside Contact Us page. 

By default Odoo provide category and sub category filter in website shop page

You can enable it from Customize-> E-commerce category on website Shop Page. 

Feel free to share your queries. 

Thanks 

Anisha Bahukhandi

Technical Content Writer

If you use Odoo Enterprise and Odoo Studio: have a look at the app Form Builder (website_form_editor). Watch also the video - https://www.odoo.com/slides/slide/form-builder-647. The video relates to Odoo 13, the modules are different and improved, but the basic mechanic is the same.

For Odoo community there are a few Odoo apps, which let do similar things from the interface as well. For example only, we developed the tool - https://apps.odoo.com/apps/modules/12.0/opportunity_custom_fields_website/ for that goals (in comparison to your requirement filters can not be applied to product selection).

If you want to introduce changes on a code level: look at the module website_crm, inherit its controller and qweb view to add new parameters.