Hi Deepthi,
What is the issue in adding a drop down ? Do you want to ask, how to start ? or you want any support on whether where to put the drop down. Every standard app can be extended based on your customer requirement and you need to check the cases.
Before enhancing, you should be first thinking, what data you want to populate in a dropdown ?
Is my odata service giving me these details ?
Which view or screen you should be enhancing ?
For your ease, you can refer below note where it talks about detailed extension for this app. Check the attachment section in this note .
2016653 - Extending the SAP Fiori apps "My Accounts" and "My Contacts"
Regards,
Tejas