Is there any archeological or written evidence for image veneration in the first few centuries especially in the ante Nicene period outside the Rome?
In terms of written evidence, there are a number of references in the Early Fathers to veneration of the Cross. This from the Catholic Encyclopedia:
Justin Martyr (d. 165) describes it [the Cross] in a way that already implies its use as a symbol (Dialogue with Trypho 91). He says that the cross is providentially represented in every kind of natural object: the sails of a ship, a plough, tools, even the human body (Apol. I, 55). According to Tertullian (d. about 240), Christians were known as "worshippers of the cross" (Apol., xv). Both simple crosses and the chi-rho monogram are common ornaments of catacombs; combined with palm branches, lambs and other symbols they form an obvious symbol of Christ.
In addition there are many depictions of Christ and the apostles in the catacombs, although it cannot be proved that these were venerated. (See "Christ as the Good Shepherd" from the Catacomb of Priscilla above.) Unfortunately for the OP's question, the best examples are in Rome.
Conclusion: the best written evidence for image-veneration in the Early Church is probably Tertullian's statement, coupled with Justin's report of widespread depictions of it, that Christians were "worshippers of the cross." We cannot be certain whether or not the many examples of Christian iconography in the various catacombs were venerated, or if they merely served as sacred decorations.
The early Church adamantly warned Christians not to treat objects made to look like gods or animals in the way pagans did. They were even encouraged to be careful to avoid stumbling other Christians due to carelessness in buying meat sold in the market that had first been presented before idols of pagan deities. See Romans 1:23-25; Acts 15:19-20 & 29; 1 Corinthians 8:7-19, 10:20-22 & 28; Revelation 2:14 & 20; 9:20, 21:8; 1 John 5:21.
All those warnings were written down by the Apostles themselves, before the end of the first century A.D. You can't get any earlier than that for the Church! Whatever later leaders of the Church said on the matter would have to agree with the Apostles' very clear warnings if they were to be true to the Christian faith.
Yes, there have been many paintings found, done by Christians, but whether they depict biblical scenes, or include animals (like Christ on the donkey, or a dove) - the question is, did the Christians revere those paintings in a way akin to worship? Did they look to those paintings to pray to who or what was depicted? There's nothing wrong with having a bit of art-work (generally speaking) but when they become bedecked with gold and jewels and silver and processed during worship, or kneeled before in private devotions, then that is exactly the sort of things the pagans did in Bible times and right through to today. Different people might define 'idols', 'icons' and 'worship' in different ways, so the only safe guide is to stick to how the 1st century Christians viewed those matters.
You ask for "any archeological or written evidence for image veneration in the first few centuries especially in the ante Nicene period outside [of] Rome". Well, of course there is, and increasingly so over the centuries following the death of the Apostles. That does not indicate it was okay to do that! It just indicates that it began to be done, and that reasons would be made to allow such practices (including redefining words), contrary to what the Apostles had stated. So, how far back are Christians prepared to go, in search of the truth about image veneration? If some support by some early church fathers is found, is that as far back as one is prepared to go? Does that give reason enough to ignore the warning of the Apostles against iconography, or idolatry (in any form or shape whatsoever)? These are important questions that spring from the fact that support of iconography and revering of objects crafted by human hands began to slip into Christian worship from an early stage, shortly after the death of the Apostles.