I don't think you need to apply for the child from Ghana. I suspect you can make a Discretionary Leave to Remain application for him, in-country.
The HO will not ask you to send a minor child overseas to apply, especially given the circumstance of your case.
He will not qualify for ILR immediately as he doesn't have a valid leave to enter and remain in the UK.
.Requirements for indefinite leave to remain in the United Kingdom as the child of a parent, parents or a relative present and settled or being admitted for settlement in the United Kingdom
298. The requirements to be met by a person seeking indefinite leave to remain in the United Kingdom as the child of a parent, parents or a relative present and settled in the United Kingdom are that he:
(i) is seeking to remain with a parent, parents or a relative in one of the following circumstances:
(a) both parents are present and settled in the United Kingdom; or
(b) one parent is present and settled in the United Kingdom and the other parent is dead; or
(c) one parent is present and settled in the United Kingdom and has had sole responsibility for the child's upbringing; or
(d) one parent or a relative is present and settled in the United Kingdom and there are serious and compelling family or other considerations which make exclusion of the child undesirable and suitable arrangements have been made for the child's care; and
(ii) has limited leave to enter or remain in the United Kingdom, and
(a) is under the age of 18; or
(b) was given leave to enter or remain with a view to settlement under paragraph 302; and
(iii) is not leading an independent life, is unmarried, and has not formed an independent family unit; and
(iv) can, and will, be accommodated adequately by the parent, parents or relative the child was admitted to join, without recourse to public funds in accommodation which the parent, parents or relative the child was admitted to join, own or occupy exclusively; and
(v) can, and will, be maintained adequately by the parent, parents or relative the child was admitted to join, without recourse to public funds.
Due to the fact that the child doesn't have a valid entry clearance or leave to remain, you will need to apply firstly for discretionary leave, and once in possession of that, you can apply for ILR on Set(F).
Registration will not be an option, until such a time as when you qualify for naturalisation. You will then apply for Registration at Secretary of state's discretion.