How to send .apk file over mobile Gmail?
Blocking .apk files and encrypted archives as email attachments is clearly mentioned in GMail policy:

To protect you against potential viruses and harmful software, Gmail doesn't allow you to attach certain types of files, including:
...

Password protected archives whose content is an archive



To protect your account, Gmail doesn't allow you to attach certain types of files...:
.ade, .adp, .apk, ...

So no one can help with that except Google. You can go with file sharing as suggested by others here, and Google as well:

If you're sure the file is safe, you can ask the sender to upload the file to Google Drive. Then send it as a Drive attachment.

Source: https://support.google.com/mail/answer/6590
But if email attachment is the only option you want to go with, use GPG/PGP encryption which is very commonly used in emails, even to encrypt whole emails including subject and body. Many e-mail clients provide OpenPGP-compliant email security. On Android you can use Termux or OpenKeychain for GPG file encryption. Both are open-source and free (I've no affiliation with either).