Formulating an analytical theory, we study phase separation of a polyelectrolyte solution under poor solvent condition confined in three types of finite geometric spaces: slab, cylinder, and sphere. Divided by a Lifshitz line, bulk polyelectrolyte solution undergoes either micro- or macro-phase separation. Confinement effects for both scenarios are studied. Composition fluctuations inducing phase separation are classified in terms of eigenmodes of the inverse structure factor operator in the corresponding geometric spaces. Tracking each eigenmode, the instability lines under confinement effects are derived in closed forms. For the confined microphase separation, we find a decaying oscillatory dependence of the spinodal point on the confinement size, which represents the commensurability between the finite period of the soft mode and the confining boundary size. For the confined macrophase separation, a typical mean-field finite size scaling of the Ising universality class is observed under the strong screening condition. (C) 2016 Elsevier Ltd. All rights reserved.