  We consider the Cauchy problem for the isentropic compressible Euler-Maxwell
equations under general pressure laws in a three-dimensional periodic domain.
For any smooth initial electron density away from the vacuum and smooth
equilibrium-charged ion density, we could construct infinitely many
$\alpha$-H\"older continuous entropy solutions emanating from the same initial
data for $\alpha<\frac{1}{7}$. Especially, the electromagnetic field belongs to
the H\"older class $C^{1,\alpha}$. Furthermore, we provide a continuous entropy
solution satisfying the entropy inequality strictly. The proof relies on the
convex integration scheme. Due to the constrain of the Maxwell equations, we
propose a method of Mikado potential and construct new building blocks.
