Can you set up Apple Watch3(Cellular) on family sharing?

A Series 4 or newer is required. The Series 3 is an older generation than the Series 4, so it will not work. No work around is known.

No;

What you need

• An Apple Watch Series 4 or later with cellular,* or Apple Watch SE with cellular, with watchOS 7 or later.
• An iPhone 6s or later with iOS 14 or later for the initial watch setup.
• An Apple ID for yourself and one for the family member who will use the Apple Watch. Your Apple ID needs to have two-factor authentication turned on.
• A Family Sharing setup that includes the person who'll use the Apple Watch. You need to have the role of organiser or parent/guardian to set up an Apple Watch for a family member.

* A cellular plan isn't required to set up an Apple Watch for a family member, but is necessary for some features.

Ask them here;

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