You can use Tapatalk BYO option which is costly or Forum Runner which is costly as well. Xenforo responsive design is quite good and will suffice well, but not in cases where users have low speed internet on their mobile devices which is extremely common in India.
Here apps like Tapatalk will come to your rescue. If you are starting out better get Tapatalk Free. I have used it for long. You can use their inbuilt ad-system as well to earn, but I am not sure of the earning potential in it.
The only forum script with a dedicated mobile app is Vbulletin if I am not wrong. But well VBulletin has long since last its charm, Xenforo has literally made them bite the dust, you can see for yourself since many large Vbulletin forums are now Xenforo boards.
What do you mean "expert in mobile app"?
The only two apps that are out are Tapatalk (BYO or branded) or Forum Runner. If you want either of those customized you have to deal with them directly.
Although, if I remember correctly, Tapatalk does have their API out so that you can custom code your own reader.
Associate your username with your license and you will get additional support in the appropriate area(s) for specific item help.
As for needing a "UI with logo" - the design of your logo is your responsibility, there are several people that do graphics related work and you can submit (once your license is associated) a request for a logo there. For customization of the actual UI of the apps - you (again) need to contact them.