Besides from their signature shoes, player jerseys are some of the most popular merchandise bought by fans. My question is, do players earn from the sales of replicas of their jerseys?
The NBA licenses its jersey sales through NBA Properties, inc., the licensing and marketing branch of the NBA. This private company negotiates deals with the various sportswear companies (such as Adidas) to produce, market, and sell the jerseys, and handles all income related to the jerseys.
NBA Properties income is included in the CBA as Basketball Related Income, and as such is redistributed to the players as part of the salary cap. It's unclear if a separate payment occurs or not; this agreement is not unfortunately public knowledge as far as I can tell. The Uniform Player Contract signs away the naming rights to NBA Properties per the Group Licensing Agreement and does not specify a payment. However, articles like this one claim that all players receive an equal cut of jersey sales. I doubt that, personally; every piece of real evidence I see suggests that jersey sales are simply part of BRI and thus each player receives their cut in proportion to their total salary.
The NBA is somewhat unique among leagues; the other three leagues reserve the naming rights to the players' association, NFLPA, MLBPA, NHLPA, and each have a separate contract. That means that players then receive a cut from that, and they are free to agree to cut that however they choose. Some players in those leagues opt out (though that seems to be rarer now).
The last player that was able to opt out, as far as I can tell, from the NBA agreement was Michael Jordan (in 1992). The Group Licensing Agreement of 1995 (which is still largely in force today) seems to have eliminated that possibility.
So the full answer to your question is: yes, NBA players receive money from their jersey sales, but it is not directly related. The jersey sales inflate the total amount of money in the league, and players receive a proportion of that (44.75% approximately, with some variance).
(Some salaries are more or less determined than others by this. Some of the 'exception' salaries for example are not really related to BRI - they're set in stone by the CBA, though their amounts undoubtedly were determined to some extent by projected BRIs. The fact that the BRI amount has dramatically risen (above and beyond what the CBA in 2011 expected, by a lot) means players playing under those exceptions are receiving less now than they were a few years ago proportionally; though of course, the increase in total cap (almost doubling) means higher quality players don't need the exceptions and probably the players getting them now would've been minimum salary guys a few years ago.)
It will entirely depend on each individual player's contract. Different leagues have different ways of licensing their names to sportswear giants.
All professional players are commercially owned by each club. In return for their service, they get a salary based on their contracts. But the details of their contracts are confidential and we can never know how they are structured. But we can safely assume that they will not earn that much from jersey sales by looking at how the system works between sportswear companies and a professional team.
NBA has a different licensing system from Premier League as this linked article indicates, Nike to become uniform, apparel provider for NBA and according to the article, LeBron Won’t Make More Money From Jersey Switch by CNBC, NBA players seem to receive money under their contracts. But, it is not clear how much is made from jersey sales.
If you are as prominent as Michael Jordan or Lebron James, you might get a lucrative endorsement outside your contract wit the team. But that's a completely different story from sales of each team's jerseys.