Is there any API to share user's login/password data between iOS app and Android app? Given I'm the owner/developer of both apps.
For Android there is Google's Smart Lock for Passwords. And for iOS there is Apple's Shared Web Credentials. These allow sharing credentials between web app and native app on the corresponding mobile platform. But I can't find any evidence that these technologies allow or not sharing between different native platforms.
If not, maybe there is another solution?
Possibly not what you want to hear but I would say this is not expected behaviour, nor is it secure. The expected behaviour would be have your user login to both platforms, after which their credentials are saved on both platforms.
There are alternative solutions however, such as OAuth. You can have user's authenticate via Facebook, Instagram or the many other popular platforms. That way the user does not need to enter a password, or remember one at all.
Another alternative could be to do instant sign in via an email link. I've seen that get popular recently. A user enters their email/username, they receive an email with a button to confirm the sign in.