Theoretically we can report dates as young as a single year, but the margin for error may be greater than the date reported. On the other hand, if the sample is too old, not enough C-14 may remain for an accurate measurement. This means that the upper limit of C-14 dating is currently around 50,000 years ago.

What is the limit in using carbon-14 as a measure to determine a fossils age?

about 50,000 years The short half-life of carbon-14 means its cannot be used to date extremely old fossils. Levels of carbon-14 become difficult to measure and compare after about 50,000 years (between 8 and 9 half lives; where 1% of the original carbon-14 remains undecayed).