  In this paper, we introduce a unified model of early and late dark energy. We
call it {\it quintessential early dark energy} model in which early and late
dark energy are explained by a single scalar field. In other words two
different energy scales are related by a single scalar field potential. To
achieve this we introduce the modified steep exponential potential. This
potential has a hilltop nature during the early time which consists of a flat
region followed by a steep region. This nature of the potential plays a crucial
role in achieving early dark energy solution. During recent time, the potential
can almost mimic the cosmological constant which can result into late time
acceleration. We also constrain and compare the models for steep exponential,
modified steep exponential, axionlike and power law potentials by using the
available background cosmological data from CMB, BAO (including DESI DR1 2024),
supernovae (Pantheon$+$, DESY5 and Union3) and Hubble parameter measurements.
The maximum improvement we get in the present value of Hubble parameter
compared to the standard $\Lambda$CDM model is for the axionlike potential. For
other potentials the constraints are similar to the $\Lambda$CDM model.
