How to approach the API design? Any Suggestions?

How to approach the API design?

I am going to start a project which will have a Web App and a Mobile App. Both will fetch the data from an API.

Now the thing is the data stored in DB is in raw format. This data would be converted to JSON and sent over the API.

Now, I have to add some new fields to the JSON API and process the existing ones. My question is should I send this data to the client and process it here or should I process it on the server. Processing the data on the client means I have to write the code two times, one for Web App and one for Mobile App. Writing the code on the server means longer wait times.

So what is the right approach?