My question is what standards, procedures our company should fulfill if we would like to design and develop medical mobile apps. Especially I am interested in design spec (UI/UX of interfaces) of those mobile apps.
Design and development of medical mobile apps should follow the local regulatory requirements in the country where you will be producing these mobile apps, and should also follow some guidance from the ISO 13485 standard. You can look at clause 7.1 Product Realization and 7.3 Design and Development for some basic guidance on the documentation. As for design specification of the UI/UX of these mobile apps, there are no standards nor other requirements, so you have to tailor them towards the intended use of the mobile apps.