The collapse of hydrophobic polyelectrolyte stars in aqueous solutions is studied using the Scheutjens-Fleer self-consistent field (SF-SCF) approach. The hydrophobic property of the segments tends to compact the stars, whereas the presence of charges has the opposite effect. As a result, star conformations can be switched from an extended, strongly hydrated, and swollen state to a collapsed state via semicollapsed, quasi-micellar state using control parameters such as the solvent quality, specified by the Flory-Huggins parameter, the pH value or the ionic strength. More specifically, there exists a range of parameters wherein the stars have an inhomogeneous radial structure with a collapsed region, referred to as the core, and a swollen region forming the corona. In such microphase segregated state the fraction of arms of the star that form the core, or alternatively escape into the swollen corona, can be controlled. The SF-SCF analysis is complemented with analytical models to rationalize the complex phase behavior.