This site started as a place to ask questions and answers about puzzles, and then expanded its scope to provide a place for puzzle fans to challenge each other with puzzles they created or found elsewhere, and likewise for others to rise to the challenge and try to solve those puzzles.
Our aim here, when posting puzzles, is about sharing either original puzzles, or ones that are very interesting that most people probably wouldn't have seen, with a community of puzzle fans.
It wouldn't be fair (nor, probably, fair use) for someone to post a stream of low quality, fairly mechanical fodder—say, a page per day from some random Sudoku book. That feels like a play to gain reputation more than to share interesting puzzles. Indeed, it wouldn't really matter if they came from a book they themselves had created or otherwise had full right to post content from; nor would it matter if the source was a book or some random generator. The repetitive content is the problem there more than the source. So it may be the case that posting even original puzzles from a book you even (co-)wrote is still not a good fit here.
However, let's assume that your book is filled with high quality, interesting puzzles. At this point we cross over into how you post beginning to be as important as what you post. Using your own material should still be given self-attribution, if for no other reason than to avoid the danger that someone decides your posts here are just plagiarizing from the book. At the same time, you'll want to make sure your notice is not self-promotion. That is to say, the attribution should be enough to convey the source and the affiliation, but shouldn't be gratuitous or overly prominent. Something like
Source: The Amazing Book Of Puzzles (and yes, I co-wrote it)
at the end of the post would work nicely. Really, it shouldn't look out of place compared to any other puzzle's attribution; you can find many examples of how people cite original sources for content they post here but did not create. Something not to do would be "if you liked this and want to see more like it, check out my book" ... yeah, that's just all kinds of not ok.
One last thought, to circle back. We should consider one last consideration: why you post. We generally prefer people not inundate the site with a burst of similar puzzles, even if they're good; it leads to genre-fatigue, and when done with a cite to a source the poster has a vested interest in, it looks like a teaser ad. And as I said at the beginning, we're really looking for puzzles that are very interesting that most people probably wouldn't have seen. Quality original content posted at a reasonable interval looks like someone contributing good puzzles to share with like-minded puzzling fans, benefiting the site and the community. But too many posts at once, or content that is uninspired or unoriginal, looks like someone trying to benefit themselves. Be mindful of the distinction and, if you're posting with the right motives, things should work out well.
Glad to have you here, and looking forward to see what you have to share!