The capital city of the kingdom of Maharaja Ranjit Singh, who was the founder of the Sikh Empire, was Lahore. Option 3 is, therefore, the correct answer.

Let`s explain the other options:

1. Amritsar: This city is significant in Sikh history but was not the capital of Maharaja Ranjit Singh`s kingdom. It is, however, the location of the Harmandir Sahib (Golden Temple), the holiest shrine of Sikhism.

2. Patiala: While this city was a princely state during the British era in India, it was never the capital of Maharaja Ranjit Singh`s kingdom.

4. Kapurthala: This is another city in Punjab, India, but it was not the capital of Maharaja Ranjit Singh`s kingdom either. It was the capital of the Kapurthala State, a princely state in British India.

In sum, Lahore (now in Pakistan) was the seat of Maharaja Ranjit Singh`s power and the capital of his kingdom.