What is the ruling of Islamic law regarding medical specializations where a female doctor mixes with men in a country that does not allow for choice between genders, and what should she do if she cannot specialize in obstetrics and gynecology?

A woman should pursue specializations that do not involve close interaction with men, such as gynecology and obstetrics, or pediatrics. If this is not possible, and she needs to study other specializations, there is no harm in it, provided she adheres to the legal hijab, avoids private seclusion with non-mahram men, and limits mixing to what is necessary and needed.