  In this paper we characterize the phase portrait of the Riccati quadratic
polynomial differential systems $$\dot{x}= \alpha_2(x),\quad\dot{y} =
ky^2+\beta_1(x) y + \gamma_2(x), $$
  with $(x,y)\in\mathbb{R}^2$, $\gamma_2(x)$ non-zero (otherwise the system is
a Bernoulli differential system),
  $k\neq0$ (otherwise the system is a Lienard differential system), $\beta_
1(x)$ a polynomial of degree at most $1$, $\alpha_ 2(x)$ and $\gamma_ 2(x)$
polynomials of degree at most 2, and the maximum of the degrees of $
\alpha_2(x)$ and $k y^2+\beta_1(x) y + \gamma_2(x)$ is 2. We give the complete
description of their phase portraits in the Poincare disk
