  We study the multifractal properties of the uniform approximation exponent
and asymptotic approximation exponent in continued fractions. As a corollary,
%given a nonnegative reals $\hat{\nu},$ we calculate the Hausdorff dimension of
the uniform Diophantine set $$\mathcal{U}(y,\hat{\nu})=\Big\{x\in[0,1)\colon
\forall N\gg1, \exists~ n\in[1,N], \text{ such that }
|T^{n}(x)-y|<|I_{N}(y)|^{\hat{\nu}}\Big\}$$ for algebraic irrational points
$y\in[0,1)$. These results contribute to the study of the uniform Diophantine
approximation, and apply to investigating the multifractal properties of
run-length function in continued fractions.
