Hi irambibi,
You need to be exercising the treaty rights in the UK in order to qualify as a sponsor of EEA permit for your wife. This means that, if you want to qualify as a student, you need a comprehensive health insurance.
If you want to qualify as a worker, this is the regulation:
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A worker is an EEA national who is exercising their free movement rights in the UK
by working in paid employment on a full-time or part-time basis.
Evidence of this may include:
• payslips dated no more than 6 weeks before the application was made
• a letter from the employer confirming employment
• a contract of employment
Assessing whether the EEA national is a worker
While there is no minimum amount of hours which an EEA national must be
employed for in order to qualify as a worker, the employment must be genuine and
effective and not marginal or supplementary.
Effective work may have no formal contract but should have:
• something that is recognisably a labour contract
• an employer
• agreement between employer and employee that the worker will perform
certain tasks
• confirmation the employer will pay or offer services (such as free
accommodation) or goods for the tasks performed
Marginal means the work involves so little time and money that it is unrelated to the
lifestyle of the worker. It is supplementary because the worker is clearly spending
most of their time on something else, not work.
I guess if you can show your payslips you should be able to prove you're a worker, but they might claim you're spending most of your time studying.
You also need to prove that your marriage is not one of convenience (as per, just getting married for the purpose of getting visa). Therefore you need to prove that you keep in contact with your wife (sending chat logs, flight tickets, pictures of you with your family and friends).