In order to get my Residence Permit for Ghana based on marriage with a Ghanaian (valid for one year, but I was told that the next permit will be valid for three years) I needed to show to the officer of the Immigration Service (in my case in Kumasi):
A Police Report (in my case a so called "VOG" issued by the Ministry of Justice in The Netherlands) to prove I have no criminal record in The Netherlands.
A "Non-Citizen Card" for Ghana, which they made for me at a state run office in Kumasi. Needed for that is your passport and filling in a form. The rest is done by them (like taking your picture and taking your finger prints). It costs about Euro 100.--. The card is valid for one year (so each year you have to have it renewed). The card is made right away (the whole process only took about half an hour or so).
Two copies of our Marriage Certificate.
Two passport photos.
Two copies of my passport.
It took three months for the Immigration Service to issue my Residence Permit. I had to leave my passport with them when I applied, but they give you written proof of your application which you can show when an official wants to see your passport during that time.
An important note/warning:
When I just arrived in Ghana in September 2022, I went to the office of the Immigration Service in Konongo, the town where we are living. There I was told that if I would marry, I could only get a Residence Permit based on marriage with a Ghanaian after more than a year, counting from the date of marriage. I was told that the only way to get a Residence Permit for the duration of a year in the mean time was to fake that I worked for a Ghanaian company. Such a permit costs US Dollar 1000.-- for one year. The Officer I talked to said he could arrange for such a faked contract through a friend when I would pay an additional US Dollar 200.--. Of course, I 'politely' refused because I know better than to get myself involved in schemes like that (getting involved in schemes like that can very easily make you vulnerable for future extorsion).
The way things eventually went, made it clear to me that one is not obliged to get one's visa extensions and Residence Permits at the office of the Immigration Service in the city/town where one actually resides (likely because there are no residence registers on city/town level in Ghana).
I would advise anyone who wants to acquire a Residence Permit to get the help of a Ghana based lawyer. I am fortunate to have a family member who is a Ghanaian lawyer, practicing in Kumasi. He took care of my two visa extensions and my Residence Permit for me. This all went very smooth.