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@Alfredo1967 wrote:

For purpose of the Child Tax Credit, Does an under 17 years old dependent  child must lived more than six months with his father (in this case) in the USA? 

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Just back up a little bit ... is the father a US Citizen or Tax Resident Alien?

If they are filing a Joint tax return, the mother is also a taxpayer.  Because the child lives with the mother over half of the year, the child meets that test.

There is no requirement for the child to live in the United States for the Child Tax Credit.  In 2021 there were some special one-year rules that involved living in the US for the refundable portion of the child, but that does not apply for the 2022 return.