[Andrew Harrington offered a link to the text of fragments 2-5 in the comments, I am adding the link here. Thanks Andrew!]
Fragment 2 as reported in 1 Clement 8:3 describes God’s mercy. Even if the sins are “redder than scarlet or blacker than sackcloth,” if the people simply call God “Father” he will forgive them. In addition to Jesus’ use of Father for God, Gal. 4:6 and Rom. 8:15 refer to calling out to God as Father (“abba”). Fragment 3 exists in several variations, but is only reported as coming from Ezekiel by Tertullian (De carne Christi 23). This saying concerns a cow which has “given birth and not given birth.” Apparently Tertullian used this as a reference to the Virgin Mary.
Fragment 4 is a saying attributed to Jesus by Justin Martyr, although it appears to come from “the prophets” in Elias of Crete and Pseudo-Athanasius.
Fragment 5 is found in Clement of Alexandria. This text describes the healing of the nation and is probably based on Ezekiel 34:14-16 and Isaiah 35:5-7. The Ezekiel passage is in the context of the true shepherd, while Isaiah describes the joy of the restoration of the people. Zeph. 3:19 and Micah 4:6-7 both use the restoration of the lame as an image of renewal.
It is too much to say these fragments had much impact on the thinking of first century Judaism, although it is clear from the writers who preserved them that early Christians read and used the Apocryphon of Ezekiel. While the Christians used texts which could be applied to Jesus as the Messiah, it is almost impossible to know how a Jewish reader would have taken these same texts.
These fragments at best indicate the currency of the idea of restoration in Judaism based on the classic texts of Isaiah and Ezekiel. The idea of a true shepherd from Ezekiel 34 may have been a popular enough of an idea that when Jesus used sheep as images in parables (Luke 15:1-3-7; John 10:11-14).
Bregman, Marc. “The Parable of the Lame and the Blind: Epiphanius’ Quotation from an Apocryphon of Ezekiel.” JTS ns 42 (1991): 125-138.
Cook, Stephen L. “The Five Fragments of the Apocryphon of Ezekiel: A Critical Study” JBL115 (1996): 532-534.
Mueller, James Raymond. “The ‘Apocryphon of Ezekiel:’ A Critical Study of Pseudepigraphic Fragments.” Unpublished Dissertation: (Ph. D.) Duke University, 1986.
Mueller, J. R. and S. E. Robinson. “The Apocryphon of Ezekiel ”in OTP 1:487-495.
Stone, Michael E., Benjamin G. Wright, and David Satran. The Apocryphal Ezekiel. Atlanta: SBL, 2000.
Wright, Benjamin G. “The Apocryphon of Ezekiel and 4QPseudo-Ezekiel” pages 462-480 in Dead Sea Scrolls Jerusalem. Jerusalem: Israel Museum, 2000.
__________. “Talking with God and Losing His Head: Extrabiblical Traditions about the Prophet Ezekiel” pages 290-315 in Biblical Figures Outside the Bible. Harrisburg, Penn.: Trinity Press, 1998.