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In this paper we consider some new classical effects obtained for a planarelectrodynamics with the presence of a higher order derivatives term. The modelcan be interpreted as a kind of extension for the $3d$ Maxwell-Chern-Simonselectrodynamics with higher order derivatives. We consider setups withstationary field sources describing point-like charges and Dirac points. Wealso investigate this model with the presence of a conducting line (in $3d$dimensions, it is the equivalent of a conducting plate in $4d$ dimensions). Inthis case we calculate the propagator for the gauge field and the interactionforce between the conducting line and a point-like charge, as well as the forcebetween the conducting line and a Dirac point, the source for vortex fieldsolutions. It is shown that the image method is not valid in any case. We alsocompare the obtained results along the paper with the corresponding onesobtained with the standard Maxwell-Chern-Simons electrodynamics [1].

Higher order derivatives extension of Maxwell-Chern-Simons electrodynamics in the presence of field sources and material boundaries