Where is iphone 13 mini serial #

On the SIM tray.

See the following from Find the serial number or IMEI on your iPhone, iPad, or iPod touch - Apple Support

Before you begin

• You can find these numbers in several places, including Settings, on the physical device, in Finder or iTunes, and on the original packaging.
• When you contact Apple for support, you can use the serial number or the IMEI/MEID number to identify your device.

and

iPhone

On these devices, find the serial number in Settings and the IMEI/MEID on the SIM tray. If you need support but you can't view the Settings menu, you can use the IMEI/MEID instead of the serial number:

• iPhone 13
• iPhone 13 mini

...