Find three rational numbers between $\frac{-3}{14}$  and $\frac{6}{14}$ .

Let's convert all the rational numbers into like terms.

$\frac{-8}{28}, 0, \frac{5}{7}$ = $\frac{-4}{14}, \frac{0}{14}, \frac{10}{14}$

$1,\frac{1}{7},\frac{-5}{14}$ = $\frac{14}{14},\frac{2}{14},\frac{-5}{14}$

$\frac{-1}{14},\frac{1}{7},\frac{5}{14}$ = $\frac{-1}{14},\frac{2}{14},\frac{5}{14}$

$\frac{-9}{14},\frac{1}{7},\frac{7}{14}$ = $\frac{-9}{14},\frac{2}{14},\frac{7}{14}$

We know that the required rational numbers have the same denominator as the rational number.

Let the three rational numbers be x, y, and z that lie between -3 and 6. 
The required rational numbers are,
$\begin{array}{l}\Rightarrow \frac{-1}{14},\frac{2}{14},\frac{5}{14}\\ \Rightarrow \frac{-1}{14},\frac{1}{7},\frac{5}{14}\end{array}$ 

Therefore, the correct option is $\frac{-1}{14},\frac{1}{7},\frac{5}{14}$.