The value of $$3\frac{1}{5} \div 4\frac{1}{2}  \text{of}   5\frac{1}{3} - \frac{1}{8} \div \frac{1}{2}  \text{of}   \frac{1}{4} + \frac{1}{4}\left(\frac{1}{2} \div \frac{1}{8} \times \frac{1}{4}\right)$$ is:

$$3\frac{1}{5} \div 4\frac{1}{2}  \text{of}  5\frac{1}{3} - \frac{1}{8} \div \frac{1}{2}  \text{of}  \frac{1}{4} + \frac{1}{4}\left(\frac{1}{2} \div \frac{1}{8} \times \frac{1}{4}\right)$$

= $$\frac{16}{5} \div \frac{9}{2}  \text{of}  \frac{16}{3} - \frac{1}{8} \div \frac{1}{2}  \text{of}  \frac{1}{4} + \frac{1}{4}\left(\frac{1}{2} \times \frac{8}{1} \times \frac{1}{4}\right)$$

= $$\frac{16}{5}\div24-\frac{1}{8}\div\frac{1}{8}+\frac{1}{4}\left(1\right)$$

= $$\frac{16}{5\times24}-1+\frac{1}{4}$$

= $$\frac{2}{15}-1+\frac{1}{4}$$

= $$\frac{8-60+15}{60}$$

= $$-\frac{37}{60}$$

Hence, the correct answer is Option A