This page will give you an understanding of the uses and some strategies of quasars.
For further information on quasars, please check the Dark Forest Wiki.
The main function of quasars is their huge base energy and silver capacity - however, they are the only celestial body within the game which do not generate any resources making them a 'battery' for your empire.
Quasars are a very niche celestial body, so generally I would advise you to ignore them. Their high energy capacity means that they spawn with far more pirates than all other same-level celestial bodies - making them tedious to take over - and their lack of resource generation (no energy, silver or artifacts) make them a lackluster addition to your empire.
Quasars are the most different of all celestial bodies with regards to their default stats. Only their range is set to the default value. For energy capacity, they have 5x the default amount and for silver capacity they have 10x the default amount. Their speed is reduced (the only celestial body to have reduced speed) and have only 0.5x of the default speed. Their energy and silver regen are both also zero (the only celestial body to have no energy regeneration).
The usages of quasars are extremely niche. Firstly, if you find yourself at peace and don’t want to start a war or expand further (generally, expansion will be more effective) you can use your excess energy and silver to begin filling up a quasar for use at a later time. Secondly, bloom filters. Since bloom filters set the energy and silver on a celestial body to 100%, usage on a quasar can give you a huge amount of resources extremely quickly. Though due to their reduced speed it may take a long time before these resources are ready to use (a wormhole of any rarity will help with this drawback).