“Have you heard of Tate Publishing? Do you think they are a reputable publisher? I submitted a children's book series and they said they wanted to publish it and sent out a contract. I am just worried because I have seen things on the internet saying that they aren't reputable and I am worried about risking the $4000 they ask for as a retainer fee. They said the $4000 is refundable once 1000 copies sell.”
Never pay a fee to a publisher—or anyone—to publish your work.
Unfortunately, there are many companies and services and “publishers” out there that prey on unpublished authors and are merely out to make a profit. They will entice authors to publish in all sorts of ways. Sometimes they will request an upfront free; sometimes they will claim they have no fees, yet later present you with hidden fees, such as “editorial” or “reading” fees; sometimes they will claim they have no fees whatsoever, yet request you buy a hundred copies of your work at a high price; sometimes they will pretend to be running a contest or competition, and request an entry fee for that contest. Later, they will claim you are a winner, and request you buy multiple copies of your published book. Legitimate publishers and literary agents will never charge any upfront fees.
I always advise authors to never pay any upfront fees to publishers, reading or editorial services, or literary agents who charge them. This is especially true in this new day and age, where authors who wish to self-publish can easily use print on demand (POD) services like CreateSpace or Lightning Source. POD services are not masking themselves as publishers. They let you know upfront that they are just printing and distribution services. With POD services, you will pay a small, one-time setup fee, and then have control of your title’s pricing and receive royalties from the first copy sold. This is not to say I advocate every author go the POD route—but rather that if you wish to self-publish, this is a much better route than paying some “publisher” an exorbitant fee upfront.
Keep in mind, too, that most authors going the self-publishing route tend to earn more money on sales from ebooks than from their paperback POD editions. In many cases, the income earned from paperback sales can be just 10 or 20% of what is earned on the ebook sales--especially in popular genres like commercial fiction. And with ebooks, there are no setup fees, especially if you can design your own jacket and convert your own file. Thus, depending on your genre, it may end up costing less time and money to focus on your ebook edition instead of the POD.