Status is the right word here.

"Attribute" is a quality or feature of someone or something: Peter had all the attributes of a first-class athlete.

"Capacity" implies holding a position or doing a job: the Princess was there in her capacity as patron of the charity. (All the examples are from the Macmillan English Dictionary.)

"Status" is a person's legal position or something person is entitled to under law (permanent resident status).

I don't think "osigurenik" is a "policyholder" or "insured person" in this context because that would be someone who has, for instance, taken out a life insurance policy.

"Osigurenik" here is almost definitely a social security/social insurance/national insurance beneficiary. So, the whole thing can be translated as e.g. "determining the social insurance beneficary status of persons employed abroad".