How is the heat capacity of alcohol is higher than mercury while alcohol, used in thermometer, is more sensitive to heat than Mercury ?
The thermal conductivity and specific heat of the working fluid in a thermometer do not affect the sensitivity of the thermometer; only the speed of response, and possibly the effect of the thermometer on the system being measured.
But alcohol has a coefficient of thermal volume expansion about $5.5$ time that of mercury.
This means that if one were to take a mercury thermometer and replace the mercury with alcohol, a given temperature change would result in $5.5$ times as much motion of the fluid in the capillary. This is the increase in sensitivity.
A liquid in glass thermometer is more sensitive to changes in temperature if for a given temperature change the change in the length of the liquid column is greater ie the scale divisions on the glass column are further apart.
The thermal expansivity of alcohol is approximately six times that of mercury so that in equivalent sized thermometers for a given temperature rise alcohol expands more than mercury and the increase in the length of the liquid in the column is greater than for mercury.