The correct answer is: British India.
The Mughal Empire was a Muslim empire that ruled over much of the Indian subcontinent from the 16th to the 18th centuries. The Kingdom of Nepal was a Hindu kingdom that ruled over the region of Nepal from the 18th to the 20th centuries. The Tibetan Empire was a Buddhist empire that ruled over much of the Tibetan Plateau from the 7th to the 9th centuries. British India was a British colony that ruled over much of the Indian subcontinent from the 18th to the 20th centuries.
British India typically exercised paramountcy (control over foreign policy and defense) over feudatory states in the region around Sikkim. This was because British India was the most powerful state in the region at the time. The Mughal Empire had declined in power by the 18th century, and the Kingdom of Nepal was a relatively small state. The Tibetan Empire had collapsed in the 9th century.
British India exercised paramountcy over Sikkim from the early 19th century until 1975. In 1975, Sikkim became an Indian state.