I really don't see what is so difficult to understand in my request. I am looking for a firm that specializes in the marketing of authors and their books. There are several online. I would prefer to get a quality referral rather than take a blind shot and hire one without foresight. If you have a good experience with such a firm I would appreciate some insight.
Oh, bless your heart.
ETA: There are lots of different ways books and authors are marketed.
Some publicists set up interviews and book signings, but then the author has to attend those events: this approach only really works if you're published by a good trade publisher, and your book has a strong bookshop presence.
Some publicists take over your social media accounts and engage with your potential readers on your behalf, but this won't be particularly effective unless you already have a huge following.
Some marketing companies deal with pre-publication work, ensuring that booksellers know about your book and that they're motivated to order it in. Again, this only really works if you're published by a good trade publisher with strong distribution in place.
Some marketing companies promise you the world but their services aren't effective.
There's a difference in marketing a new release vs an author's backlist.
Yes, I can give you a list of well established marketing and publicity companies, but they're not necessarily going to be able to help you and without knowing more about who you are and what you want to achieve, and how your books have been published, I won't be able to be sure that the publicists etc. will be appropriate for your works.
If your books have already all been published, you're going to struggle to market them now. It might be better to wait until you have a new release, and then go all out to market and promote that book, along with your backlist.
I used to work in sales and marketing, and have a lot of experience and connections. But your snarky response to my question makes me wonder how well you'd deal with the hard and stressful work required to promote a book well.