Could there be a planet at the barycenter between two or more stars revolving around each other?
No.  Such an arrangement is at best &quot;metastable&quot;.  That is, although there are periodic solutions to the three body problem (stable orbits) an infintesimal perturbation (eg the proverbial butterfly flapping its wings) will push the system off the stable orbit and into chaos.  Getting a planet to remain at the barycentre is like trying to balance a pencil on its sharpened point.
With two bodies, each orbits around the barycentre.  But with three bodies, the bodies don't orbit around the three-way barycentre. And a planet placed near the barycentre of two stars will not tend to remain in orbit around that point.
The Lagrangian point L1 is also at best metastable. Satellites that orbit the sun at the Earth-Sun Lagrangian point need to fire their engines and do regular &quot;station keeping&quot; to keep them from drifting away.
The L4 and L5 points can be stable. Bodies at the L4 and 5 points are called &quot;Trojans&quot;.  However no Trojan exoplanets are known.  A Trojan planet would see the two stars separated by (a variable amount averaging at) 60 degrees