Ok, I thought you might be using the term "mutation" in this sense.
In biology mutations refer to changes in DNA (copying errors) that occur during cellular replication. If such a mutation occurs during the production of reproductive cells, those mutations become part of the offspring's genome. Every organism that reproduces will have offspring with mutations in them. For example, humans are estimated to have about 50 to 100 or so unique mutations compared to their parents.
However, you won't find mutations changing an organism into something completely different (e.g. a different species) in a single generation. If you take human evolution for example, we are thought to share a common ancestor with chimpanzees going back around 5 million or more years. That means it took several hundred thousand generations to go from a chimp-human ancestor to what we are now. There was no single generation steps; it was the accumulation of changes in hundreds of thousands of generations.
What we see in the fossil record are snapshots of organisms that were part of this lineage at different moments in time. In many cases those moments in time are separated by hundreds of thousands or even millions of years; long enough for changes to accumulate.
Transitional fossils are simple fossils that are part of that lineage; fossils that specifically show a change in morphological features in between taxa. And given we have fossils that show just that, by that definition transitional fossils do exist.
