Visa for Child (2 yrs) born outside UK - both parents have ILR

Hello all,
I will appreciate some form of guidance.
1. I arrived UK in 2009 as a student. I moved on tier 2 sponsorship in 2013. April 2018 I applied for ILR and a year later April 2019 applied for naturalization. Application for naturalization is pending.

2. While on Tier 2 sponsorship, my spouse joined me in UK in 2014. This March 2019, she applied for ILR and she's was successful. Both of us now have ILR.

3. We had our son in USA, Oct 2016. At the time none of us have ILR. He was brought into UK Feb 2017 as a visitor. Applied for him to become a Tier 2 child dependant in Dec 2017. Therefore, 10 months spent as a visitor and 1 year 4 months on Leave to Remain as a dependant.

4. In all cases, Tier 2 sponsorship visas would have expired May 2019 but i moved into ILR so is my spouse. Now, only my son is remaining as a dependant on this visa, which is running out in few weeks.

5. My question: What visa should i be applying for him? I cant find a definitive guidance on this.
a.) Can i apply for registeration for him on discretional basis ? (One parent already applied to naturalise and the other settled).
b.) Should i be applying for a further leave to Remain?
c) should i be applying for ILR ?
I am hoping to avoid unnecessary immigration payments if i can circumvent it.

6. if my naturalisatio application is approved and i become a citizen before the expiration of current his LR, can i register him as a child of a citizen? I understand my wife will automatically qualify to naturalise at this point.

ILR on form Set f.

You could have included the child with your wife's ILR.

Children born abroad are expected to hold ILR before applying for citizenship.

Oh thanks for your prompt reply.
I didn't realise he would be qualified for an ILR at the time. We thought he need to be more than 5 years old to meet the 5 years requirement.

Out of curiosity, my wife used the super priority (next day decision) costing additional £800.

Supposing i have added my son to the application, will that single payment of £800 cover both of them in the joint application or each have to pay £800 making it £1600 extra for the super priority service?

I didn't realise he would be qualified for an ILR at the time. We thought he need to be more than 5 years old to meet the 5 years requirement.

There is no 5 year residence requirement for PBS dependent children.

Out of curiosity, my wife used the super priority (next day decision) costing additional £800.

Supposing i have added my son to the application, will that single payment of £800 cover both of them in the joint application or each have to pay £800 making it £1600 extra for the super priority service?

My understanding is that the fee is per person applying.

I am surprised HO did not write to you to ask about the child that was not included with your wife's application.