Personally I wouldn't bother looking for a litter of puppies. You should look for a breeder.
You need to decide what matters for you in terms of a credible breeder. For example do you just want to ensure that it is not a puppy farm or do you want a breeder who is trying to better the breed. They are not the same thing.
I use to source dogs as part of my job. The main priority for my workplace would be finding a litter that was healthy. Secondly would be behaviour. So the first step would be to find out all the health and behaviour concerns listed for a breed. Don't just look at the kennel club because currently they don't recommend any checks for Yorkshire Terriers, really do your research. Speak to your vets, do a Google search and look in a good quality dog book, I would usually make a list. Then find out what the relevant tests for all these health problems are. Then I would go through the list and highlight which health problems are the most important to have checked for me and which are not as important. For example Yorkshire Terriers are prone to Chiari malformation Syringomyelia which can be screened for by MRI, equally they are notorious for having terrible teeth. Therefore if I was looking for one my main requirement would be an MRI test and I would be willing to expect I may have some dental bills in my future. In all honesty as the kennel club doesn't recommend any health tests for this breed you will probably struggle to find a breeder who has tested. So this is why you will need to be aware of what health requirements you have. That way you can search for breeders who do test but equally you're aware of what you could get yourself in to. When I look for a breeder I tend to prioritise health concerns with no cure so for example the Chiari malformation Syringomyelia, I would not want to watch a dog suffer.
After I had done all of that and found a breeder who met my health criteria I would then have to investigate the litter. Firstly I would have to investigate the inbreeding coefficient for the litter, this can be done on the kennel club's website and is very simple. You enter both parent's names and then it will generate a number. The lower the number the less inbred the dog. This means the genetic issues should in theory be smaller because the gene pool is larger. This is also a good way to check that the breeder is registered and the puppy is not imported.
Only after all of that would I even contact the breeder. Then I would have a long list of questions, mainly centred around health and behavioural. It's also good to ask how long they've been breeding, how many litters they've bred, how many dogs they own, whether or not they show, why they breed. You want a large picture so you can determine whether or not they are a puppy farm.
If I was happy speaking to the breeder after the phone call then I would go and see the litter. I would pay close attention to the mother and any other dogs at the premises, the house, the breeder. In my personal experience a caring breeder has many dogs, whom they have dedicated their lives to. Their entire home will be covered in hair probably as well as many pictures and ornaments of their breed. A caring breeder would also be able to tell you about the puppy's personality, and the mothers and any other dog in their care. I would also ask to see copies of the health tests. I would also ask what vets they are registered at. During this meeting I would expect to be asked as many questions about myself as I am asking about the breeder.
After my visit I would then ring the vets they are registered at to check that they are. Puppy farms don't tend to register, I would also ask the vet general questions 'would you consider x to be a responsible breeder' 'are x's dogs cared for suitably.'
If all of this was ok only then would I purchase a puppy. I do hope you find this helpful.