Jason Hare wrote:οὐκέτι πολλὰ λαλήσω μεθ’ ὑμῶν, ἔρχεται γὰρ ὁ τοῦ κόσμου ἄρχων· καὶ ἐν ἐμοὶ οὐκ ἔχει οὐδέν.
Seems to me he's saying that he doesn't have much more to speak with his disciples, since his time is limited and the ruler of the world (that is, Satan) was coming — to bring worldly judgment on him. Although he is called "the ruler of the world," Jesus was claiming that there was nothing within himself over which Satan had any power. "He has nothing within me."
It is, I guess, surprising that this wasn't said more directly as, perhaps, καὶ ἐπ᾿ ἐμοὶ οὐκ ἔχει ἐξουσίαν or something similar.
Considered in isolation, I agree that "no claim" seems plausible, but where is the sense to it. It is like this conversation:
Bob: "Peggy, I can't marry you."
Peggy: "But, Bob! Why not?!"
Bob: "Because the University Dean has no claim on me."
It seems a bizarre non-sequitur. In fact, the opposite would make more sense:
Bob: "Peggy, I can't marry you."
Peggy: "But, Bob! Why not?!"
Bob: "Because the University Dean has a claim on me."
BDAG suggests "has no hold on me", which again makes the conversation bizarre:
⑨ special combinations
ⓐ w. prep. ἐν: τὸν θεὸν ἔ. ἐν ἐπιγνώσει acknowledge God Ro 1:28 (cp. ἐν ὀργῇ ἔ. τινά=‘be angry at someone’, Thu. 2, 18, 5; 2, 21, 3; ἐν ὀρρωδίᾳ ἔ. τ. 2, 89, 1; ἐν ἡδονῇ ἔ. τ.=‘be glad to see someone’ 3, 9, 1; ἐν εὐνοίᾳ ἔ. Demosth. 18, 167). ἐν ἑτοίμῳ ἔ. 2 Cor 10:6 (ἕτοιμος b). ἐν ἐμοὶ οὐκ ἔχει οὐδέν he has no hold on me J 14:30 (Appian, Bell. Civ. 3, 32 §125 ἔχειν τι ἔν τινι=have someth. [hope of safety] in someone). κατά τινος: on 1 Cor 11:4 s. above 4. ἔ. τι κατά τινος have someth. against someone Mt 5:23; Mk 11:25; w. ὅτι foll. Rv 2:14. ἔ. κατά τινος w. sim. mng. Hm 2:2; s 9, 23, 2; w. ὅτι foll. Rv 2:4, 20. ἔ. τινὰ κατὰ πρόσωπον meet someone face to face Ac 25:16. μετά: ἔ. τι μετά τινος have someth. w. someone κρίματα lawsuits 1 Cor 6:7. περί: ἔ. περί τινος have (a word, a reference, an explanation) about someth. B 12:1; with adv. τελείως 10:10. πρός τινα have someth. against someone (Ps.-Callisth. 2, 21, 21 ὅσον τις ὑμῶν ἔχει πρὸς ἕτερον) Ac 24:19. ζητήματα ἔ. πρός τινα have differences w. someone (on points in question) 25:19. λόγον ἔ. πρός τινα 19:38. πρᾶγμα (=Lat. causa, ‘lawsuit’: BGU 19 I, 5; 361 II, 4) ἔ. πρός τινα (POxy 743, 19 [2 b.c.] εἰ πρὸς ἄλλους εἶχον πρᾶγμα; BGU 22:8) 1 Cor 6:1. ἵνα ἔχωσιν κατηγορίαν αὐτοῦ J 8:4 D (cp. 5 above). πρός τινα ἔ. μομφήν have a complaint against someone Col 3:13.
ⓑ τοῦτο ἔχεις ὅτι you have this (in your favor), that Rv 2:6. ἔ. ὁδόν be situated (a certain distance) away (cp. Peripl. Eryth. 37: Ὡραία ἔχουσα ὁδὸν ἡμερῶν ἑπτὰ ἀπὸ θαλάσσης) of the Mt. of Olives ὅ ἐστιν ἐγγὺς Ἰερουσαλὴμ σαββάτου ἔχον ὁδόν Ac 1:12.—ἴδε ἔχεις τὸ σόν here you have what is yours Mt 25:25. ἔχετε κουστωδίαν there you have a guard (=you can have a guard) 27:65 (cp. POxy 33 III, 4).
Arndt, William ; Danker, Frederick W. ; Bauer, Walter: A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago : University of Chicago Press, 2000, S. 422