I got a job in a company where there are handling hosting support for data centers(support for other hosting company's servers) and my job involves remote linux server (management)administration where we solve web server issues and host customers web site on web servers,we are taking care of mail server,DNS server and also mysql servers.As i am working in rotational shifts in 24/7support center my question is after 2 years if i relieve from this company will i get jobs only in web hosting support companies(24/7 schedule) or can i get job as server admin in a single company where they manage their own server in managing other regular backup login details of their company's employees etc., because i cannot work in rotatory shifts for my whole life i am asking this question.

If you have experience and enough knowledge of handling web servers, there is no reason why companies should not hire you. More important is the role that you play.

You can do your own business but it depends on you

Working 24/7 shift and standby based is always the start of most IT professionals...if you perform well and prove yourself there's no reason that you won't get the kind of job you describe.