Can u sign up for Apple care after 60 days of buying my phone ?

No.

How to buy

Purchase either AppleCare+ product with your new iPhone.

Or buy it within 60 days of your iPhone purchase:

On your device (go to Settings > General > About and choose AppleCare+ Coverage Available)

Online (requires you to verify your serial number and run a remote diagnostic)

At an Apple Store (inspection of iPhone and proof of purchase are required)

By calling 800-275-2273 (requires you to run a remote diagnostic and provide proof of purchase)

https://www.apple.com/support/products/iphone/

Dng_8 wrote:

Can I sign up for Apple care after 60 days of buying my phone ?

No. Apple allows you to purchase Applecare+ for 60 days after your purchase.

https://www.apple.com/ca/support/products/iphone/