Regarding the Field Level Encryption and partial search over encrypted field.

We are doing a partial match with $regex expression with $match in the aggregation pipeline and returning results matching with the regex on name, mobile, and email. We want to do encryption for mobile and email with automatic FLE provided by MongoDB.

is there any way to achieve this ?, because $exps and $regex are not supported in FLE as per the documents.

No. In a future version of Queryable Encryption we plan to provide a substring search capability, but not $regex over encrypted data. The problem is that leaks far too much information about the plaintext from the ciphertext.