What direction is current for an electron in both $E$ and $B$ fields?

No matter what fields exist in space, electric current is always in the direction opposite to the direction of motion of e-, because e- are negatively charged particles.

However, current is not defined for a single e-, because current is a continuous flow of charges. But if we have to tell the direction of current anyways in case of a single e-, we would say it is in the opposite direction.

In the image attached, electric current means that if a positively charged particle is moving in that direction, B is in that direction, then Force will be in this direction.

If an e- is moving in the same direction as the positively charged particle was moving, then direction of force will rotate 180 degs

Fleming's right hand rule (as shown in your image) is just a mnemonic for the cross product in the formula $$F=Ivec{ell}timesvec{B}$$ where $vec{F}$ is the magnetic force acting on a piece of wire, $I$ is the current, $vec{ell}$ is the length of the piece of wire, and $vec{B}$ is the magnetic field.

This magnetic force on a current-carrying wire is actually a consequence of the Lorentz forces acting on all the electrons moving within the wire.

The Lorentz force on a single particle is $$vec{F}=qvec{v}timesvec{B}$$ where $q$ is the electric charge and $vec{v}$ is the velocity of the particle.

Remember that an electron is negatively charged (i.e. $q$ is negative) and therefore its velocity is opposite to the direction of the current.

So therefore you can use the same right hand rule for ($vec{F}, qvec{v}, vec{B}$) like you did for ($vec{F}, Ivec{ell}, vec{B}$).