Hello, Guys!

Is there any trusted Email (except Yahoo!) in the World which sends every E-Mail notification/new email on Mobile using Mobile Career only?

I want suppose if an E-Mail comes to my Inbox then it should (right on time) come to my Mobile using Mobile Career not Internet. Example: A man has sent you an E-Mail. Plz check it online.

My Mobile Career is Zong in Pakistan.Please understand I , or anyone, can not give you a  answer a to your question.
However, there are some considerations you may wish to REVIEW and can help   make a reasonable decision.
Here is a quote I found doing some research recently:
Quote

Countries with restricted access

Google restricts access to some of its enterprise services in certain countries, such as Cuba, Iran, North Korea, Sudan, and Syria. If you try to sign in to these services from these countries, the FOLLOWING error appears:

You appear to be signing in from a country where Google Apps accounts are not supported.
If you try to sign up for these services from these countries, the following error appears:

You appear to be signing up from a country where Google Apps accounts are not supported.
Certain Google services, such as Gmail, might be available in these countries for personal use but not for enterprise use.

(Fox News , Published December 14, 2012Associated Pres)
Internet censorship, restrictions around the globe
DUBAI, United ARAB Emirates –  Envoys in Dubai signed a new U.N. TELECOMMUNICATIONS treaty Friday that a U.S.-led delegation says endorses greater government CONTROL of the Internet.

The U.S. and more than 20 other countries refused to ratify the accord by the 193-nation International Telecommunications Union.

Here is a look at Internet restrictions and availability at selected countries and regions around the world:

Please understand I , or anyone, can not give you a  answer a to your question.
However, there are some considerations you may wish to review and can help   make a reasonable decision.
Here is a quote I found doing some research recently:Of course, your country is not specifically listed.For the list, Look Here:

If I knew the answer, I would  give it  to you in a private message.

Off topic, I think the United Nations will take steps to help protect the rights of people and  prevent insurrections. What I think matters little. Time will tell.