Thanks for your question.
If you are a UK National (by descent) and are living in the UK and have recently had a child with your partner, your child would be entitled to obtain UK Citizenship.
If the child was born outside the UK, then you would not have been able to pass on your UK Citizenship as you obtained it by descent.
If you wish to discuss, please feel free to ask further questions.
Yes you do need to be a resident of the UK. If your wife is in the UK and you are not, your child will not be automatically eligible for UK Nationality.
Your child would be able to obtain UK Nationality if he/she spends the first 10 years of their life in the UK. As per the details on the link provided above.
Resident would mean that you would be living in the UK for at least 6 months of the year. (Often referred to as 'habitually resident')
If you live with your child in the UK then the child will require only 3 years, if the child is on their own, they will require 10 years.
From all of the information you have provided above and considering the fact that you are not resident in the UK, I am of the opinion that your child will not automatically be entitled to UK Citizenship.
If you move to the UK permanently in the future, the child will be able to obtain Citizenship after 3 years.
I am not sure what else I can say to convince you.
The rules on the following link, make it clear in what circumstances a child can apply for Naturalisation as a UK Citizen.
If a child's parents are settled in the UK, then the child will be able to apply for Naturalisation as a UK Citizen. You have stated above that you are not settled in the UK and thus, the child would not be entitled to apply for Naturalisation unless the parents were settled in the UK.
The fact that one parent has obtained Citizenship by descent would mean that the citizenship would not automatically pass to the child unless the child was born in the uK to UK National Parents who are settled in the UK.
I hope this helps.
Section 1(3) applications - children born in the United Kingdom to parents who are now settled in the United Kingdom
If the child's parent becomes SETTLED in the UK, the child would be entitled to register as a UK National, From what you have stated above, it seems that you are not SETTLED in the UK but merely visiting.
As you are not SETTLED, the child would not automatically obtain UK Citizenship.
Only one parent needs to be settled in the UK. To be settled in the UK would mean that you are living in the UK permanently. A person with a travel visa is not SETTLED in the UK.
You will need to show that you are living in the UK and registered on the electoral roll. This should be sufficient.
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