How to convert png to GeoTIFF?

Question

Google Maps

There is a bitmap in .png. Image - a custom piece of the map, for a certain zoom level, for a certain area.
Task: to make sure that in a mobile application for iOS, the standard Apple map engine shows my image for the area I need.
Until the end of the topic has not yet figured out, but began to move in the next direction:

1. I want to use MapBox in the tile provider class.
   
2. Using Mapbox Studio to create a map, for this I need to add a layer with my image.
   Problems arise at this stage:
   
   • a) I can't convert png to GeoTIFF, more precisely I can convert, but the studio doesn't want to "eat" such TIFF. Converted using QGIS.
     
   • b) I can't figure out where I should set the coordinates of the area that should be covered by my .png. In GeoTIFF metadata?
     
   
   

I think that there are many options for solving the problem, if I went along a difficult or wrong path, direct me to the true path.
Using the Apple map engine is optional.
Using MapBox is optional.

Answer 1

I can't tell you anything about Apple Mapkit, but about creating a tiled data source, I can.
To get a map from PNG to GeoTIFF, you really need to use QGIS, just not just open and save the file, but use the Georeferencer module to bind the image to coordinates. This is described here, for example: https://docs.qgis.org/2.2/en/docs/training_manual/...
To correctly complete this task, you need to know the coordinate system of the map and the coordinates of several points on the map.

Answer 2

option 2: take a global mapper, attach a picture and cut it into tiles