Hey there, dantonb14
Thanks for reaching out on Apple Support Communities regarding your mail not syncing between devices. I’d be happy to help!
It sounds like your mail is not syncing when making changes from your laptop to your iPhone. I’d recommend checking Settings > Passwords & Accounts > Fetch New Data. From there, you can see if your email accounts are set to Push, Fetch, or Manual. You can also change how often the device will fetch data.
You can also check to ensure that your Mail settings are correct by using: Mail Settings Lookup To see if the settings match what is on your iPhone, go to Settings > Passwords & Accounts > Tap email account > Advanced.
You can also test to see if this occurs on a particular network or on specific devices. For example, does it only happen when using cellular data or when on your home network?
Let us know the results and take care!