I’m sure about this one, King Crescent. They have worked with brands like Nauti Nati, Hopscotch India, Asos etc. Work is finished in time, everything is done systematically. I never faced any issue working with them and only learned so much more about online marketing.
I used to work with this company https://light-it.net/#1/ and pretty sure they can help you. I had an online project and badly needed web developers who could understand the specific of it. They turned to be very professional and made my online business profitable by developing the best crm system I have ever seen
I think that there are quite a lot of them and to choose one you need to get familiar with their approach, methodologies and samples to understand what you will get. Also, I recommend you to check out an article here, it's about responsive web design testing and if you have a serious business, your website just needs to be responsive.