MOSFET – Body Diodes in MOSFET Symbol

The body diode is part of the MOSFET structure and is always there. Sometimes a Schottky diode is added (co-packaged) because the body diode is slow recovery. Since the Schottky diode has a lower Vf it conducts most of the current.

It should be noted that the diode only comes into play in a configuration such as a half-bridge or H-bridge where the diode conducts when a different switch turns off. The internal diode is in the wrong place for a single switch controlling an inductive load- when the switch turns off the voltage across the switch rises rather than reversing.

The parts on that schematic are very low capacitance (and, unfortunately, that generally means relatively high 'on' resistance) compared to the otherwise nice ones that Ignacio mentions in his comment.

The switch is designed to have low charge injection since that directly affects the accuracy of the nulling.

You might consider something like the ADG5236 in a modern design, which has 0.6pC of charge injection, which is only 60nV on a 10uF capacitor.

Or use an amplifier that has the autozero circuitry internally, but I see you're actually working on a sample-and-hold circuit.