In this paper, an on-chip photonic sampled and quantized analog-to-digital converter (ADC) on thin-film lithium niobate platform is experimentally demonstrated. Using two phase modulators as a sampler and a 5$\times$5 multimode interference (MMI) coupler as a quantizer, an 1 GHz sinusoidal analog input signal was successfully converted to a digitized output with a 20 GSample/s sampling rate. To evaluate the system performance, the quantization curves together with the transfer function of the ADC were measured. The experimental effective number of bits (ENOB) was 3.17 bit. The demonstrated device is capable of operating at a high frequency up to 70 GHz, making it a promising solution for on-chip ultra-high speed analog-to-digital conversion.