Can I download iOS 15 using data

Installing iOS by using a cellular data connection requires an iPhone 12, 13 or 14 and a 5G data plan and 5G connection.

If you meet the hardware requirements, go to Settings/Cellular/Cellular Data options/Data Mode/ and enable "Allow More Data on 5G"

But, if your iPhone can install iOS 16, you can't install iOS 15. It will always install the highest possible iOS version.

Generally, updates are avail ONLY via 5G “mobile data.”

If you’re updating to iOS 15x … your phone unfortunately doesn’t have 5G capability.

You’ll need either WiFi or a computer + cable.

See:

Update your iPhone or iPad - Apple Support