I am searching for cheap hosting company with 24 hour support. My current hosting provider does not provide online support during night, that is why I am planning to migrate to another hosting company.
You did not give your site(s) requirements, do you need root access? just standard shared hosting? windows? linux?
Yes if you post your requirements it will be alot easier find what plans you are looking for. Theres alot of web hosting on this forum that can provide support 24/7 by phone and chat.
As you are looking for a Hosting provider who offer 24X7 support even on weekends and midnight, so you can search over Internet for them. Once you find one, you can call them on weekends or at midnight to check if they really offer what they have advertised. This is the best way to check their reliability. Once you are satisfied that they offer what they have advertised then you can opt for their services.
Or you can just go with a larger reputable provider so you don't have to stay up one night for no reason
Most larger "reputable" providers like GoDaddy, Host Gator, 1&1 etc do offer cheap shared hosting plans with 24x7 phone/chat/e-mail support.
There are lots of hosting company to choose from and most of them offer 24/7 customer support. Before you buy on one company, call them on wee hours or on weekends if they truly are 24/7.