Hi @Lukasz_Krason-Becker and welcome to the forum!
Currently, as you observe, it’s not possible to display custom fields in the My Tasks view.
Asana has said that they will soon be updating the My Tasks view so that it works a lot more like a regular project. Whether that will include the ability to have custom fields, we don’t know yet - we’ll have to wait and see once that update occurs.
In the meantime, you can add your vote for custom fields in My Tasks here: