When citing papers which use the different notation for the same
model, is it better to leave the notation as is when citing each
source, or, to retain consistency conform to one notation?
It is extremely important to maintain notational consistency within your own paper; never double-up on notation or give inconsistent notation within your paper. As to where your notation should come from, as a general principle, you should use whatever notation is easiest for the reader, whether this is taken from another paper, or your own adaptation or invention.
Bear in mind that established fields tend to have notational conventions that people are used to, so if there are symbols commonly used for particular objects, it is generally best to use these unless there is a good reason to the contrary. When notational conventions from multiple fields conflict (e.g., you are doing a paper on random matrices, and the capitalisation conventions for probability conflict with the capitalisation conventions for linear algebra) you will need to make judgments as to what is easiest for the reader.
If I were to conform to one notation, does the more recent source take
priority when choosing notation or the earlier source? Additionally
how would it be formatted when quoting the source with the altered
There is no temporal priority rule for notation, but bear in mind that if a new notation is sufficiently well-established, it may constitute the current notational convention (check multiple papers for this, not just one newer one). When quoting a result from another paper, in your own altered notation, you should add some parenthetic remark to make the reader aware of the change:
Example: Wilbur (2009) notes that "...if A and B are engaged in exclusive contractual negotiations, and C interferes with this process, causing economic harm to B, then C could be liable for tortious interference" (p. 85, notation altered).