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You don't mention the device you are using for your mobile broadband. I would put this down to your device email settings. Please refer to device guides here: Device Guides
I have moved this thread to the correct board @Maroc where you will receive a better response. There may be other members on the forum with an i phone who will be able to give you a better reply.
At a guess this will be connected to your i messages. Make sure mobile data is turned on in your message settings.
What happens when you try to send an e-mail from your handset, do you get any error messages? Are all your other apps and web browsers working when connected to mobile data? Also, have you ever been able send or receive e-mails on 4G? Can you check the link here, this will show you the correct internet settings for your phone.
I am now able to send E-mail but NOT receiving Emails
Every time I open the outlook app and refresh for new messages , all I am getting checking for Mail
I have switched off and on my devise but nothing has changed
Also to add , this issue only started lately , two to three weeks ago
Before I used to send and receive E-mails with no problems