One of parent going to get PR and Infant need UK citizenship

Dear All,
Greetings !!

My wife is going to apply for PR in the month of Oct, 2019 on 10 year route. We both are Indians, our son was born on 25 Oct 2018, till now we got only his birth certificate. Kindly clarify how to get him UK passport.
People are telling first we need to apply for naturalisation and apply for passport once after mother getting PR.
Some are telling directly we can apply for UK passport once mother get her BRP of PR and no need for naturalisation.
Kindly advice or share the link information for fee to apply for naturalisation and UK passport.
Thank you all !!

You mean ILR based on 10 years long residence and not PR. Note that PR is granted under the EEA/EU rules.

What is your immigration status in the UK??

Kindly clarify how to get him UK passport.

Only a British citizen can apply for a passport. Your child is not British. Presumably your child was born in the UK and not abroad??

People are telling first we need to apply for naturalisation and apply for passport once after mother getting PR.

You apply to REGISTER the child as British on form MN1, it costs £1023. Passport is separate after the child is registered as British. Naturalisation is only for adults.

Some are telling directly we can apply for UK passport once mother get her BRP of PR and no need for naturalisation.

No you cannot. This would only apply if the child was born AFTER either parent was granted ILR. Only a British citizen can apply for a passport.