They want to sit on the right and left of Jesus (Mk 10:37-10:37)

“They said

To Jesus.

‘Grant us

To sit,

One at your right hand

And one at your left hand,

In your glory.’”

 

οἱ δὲ εἶπαν αὐτῷ Δὸς ἡμῖν ἵνα εἷς σου ἐκ δεξιῶν καὶ εἷς ἐξ ἀριστερῶν καθίσωμεν ἐν τῇ δόξῃ σου.

 

There is something similar to this in Matthew, chapter 20:21, but here the brothers, rather than their mother spoke with Jesus.  Mark said that the 2 brothers responded to Jesus (οἱ δὲ εἶπαν αὐτῷ).  They wanted him to let them sit at his right hand (Δὸς ἡμῖν ἵνα εἷς σου ἐκ δεξιῶν) and at his left hand (καὶ εἷς ἐξ ἀριστερῶν καθίσωμεν) when Jesus came in all his glory (ἐν τῇ δόξῃ σου).  After all, they had been with Peter at the transfiguration and were among the four original disciples.  Thus, they were already very special.  Perhaps, they thought of this as an earthly kingdom.  Ironically enough at the crucifixion of Jesus, it would be two thieves on the right and left side of Jesus.