Wikipedia:
When the areas were being established, the boundaries were deliberately drawn to avoid centres of population. Approximately 18,195 people live in the areas. About 11,000 native Cypriots work in the areas themselves, or on farmland within the boundaries of the areas. The British military and their families make up the rest of the population.
Persons related to the territory may in theory be eligible to claim the British Overseas Territories citizenship (BOTC status) through a personal connection to the areas (i.e., birth on the territory before 1983, or born after 1983 to a parent who was born on the territory before 1983). But unlike most other British Overseas Territories, there is no provision in the 2002 amendment of the British Nationality Act 1981 by which British citizenship (with the right of abode in the United Kingdom) can either be claimed through automatic entitlement or be applied for by means of registration, from or through a sole personal connection to the Base Areas (in comparison, the 2002 Act bestowed British citizenship on all other BOTCs). Hence, non-British and non-military personnel with the connection to the territory cannot live and work in the UK and must use their Cypriot passports to apply for visas to the UK.
Under the terms of the 1960 agreement with Cyprus establishing the Sovereign Base Areas, the United Kingdom is committed not to use the areas for civilian purposes. This was stated in 2002 as the primary reason for the exclusion of the areas from the scope of the British Overseas Territories Act 2002. As of 2010, around 7,195 service personnel of British Forces Cyprus are based at Akrotiri and Dhekelia.
搬运其中一个回答：
The children of British personnel serving in Cyprus irrespective of where they are born get British citizenship. They don’t have the right to Cypriot citizenship. Children of British ex-pats born in the Republic have the right to Cypriot citizenship.
Children of Cypriots born in the sovereign British bases area automatically are Cypriot citizens and do not have the right to British citizenship.
Cypriots born in Cyprus prior to 1960 and left Cyprus prior to 1960 have the right to British and Cypriot citizenship.
Cypriots born in Cyprus prior to 1960 but remain in Cyprus after the establishment of the Republic in 1960 automatically became Cypriot citizens and lost the status of British subject unless expressively declare they refuse Cypriot citizenship in which case they were to vacate the republic.
TLDR就是，如果是英军的孩子就是英国国籍；如果是塞浦路斯的村民，孩子也是塞浦路斯国籍。
