  We study the influence of external electric and Zeeman fields on the
Josephson response of a planar superconductor/altermagnet/superconductor
junction. We show that the critical Josephson current across the junction
oscillates as the altermagnetic field strength increases. The current-phase
relation can be forward- or backward-skewed due to significant second-order
Josephson response. It decisively depends on the altermagnetic field strength.
We discover that the skewness can be manipulated by electric gating. We reveal
two additional impacts of external fields on the Josephson current: (i) Fields
can induce 0-$\pi$ transitions. (ii) Fields can substantially enhance the
critical current.
