  Superconductivity and magnetism are mutually exclusive in most alloys and
elements, so it is striking that superconductivity emerges around a magnetic
quantum critical point (QCP) in many strongly correlated electron systems
(SCES). In the latter case superconductivity is believed to be unconventional
and directly influenced by the QCP. However, experimentally unconventional
superconductivity has neither been established nor directly been linked to any
mechanism of the QCP. Here we report measurements in the heavy-fermion
superconductors CeIrSi$_3$ and CeRhSi$_3$. The measurements were performed with
a newly developed system, first of its kind, that allows high-resolution
studies of the superconducting gap structure under pressure. Superconductivity
in CeIrSi$_3$ shows a change from an excitation spectrum with a line-nodal gap
to one which is entirely gapful when pressure is close but not yet at the QCP.
In contrast, CeRhSi$_3$ does not possess an obvious pressure-tuned QCP and the
superconducting phase remains for all accessible pressures with a nodal gap.
Combining both results suggests that unconventional behaviours may be connected
with the coexisting antiferromagnetic order. This study provides a new
viewpoint on the interplay of superconductivity and magnetism in SCES.
