None is more fundamental, they are concepts for describing phenomena, but they cannot be tested at a fundamental level. However, some are more general than others...
The concept of force is historically older, originated by ancient philosophers, but in Newton we see the most useful conception of force, who understood that in its absence, motion can occur. This conception changed drastically the previous idea that no motion can occur without force, which seems a natural notion from human experience. Newton was also the first that introduced the notion of non-contact force, by explaining gravity as a universal action at a distance force. This however does not make force a fundamental concept, but rather a very powerful because it allows explaining and quantifying so many phenomena.
The concept of field is introduced much later, and was necessary because the notion of force was not sufficient to describe electromagnetic phenomena. When using the idea of force in explaining electromagnetic phenomena, we had to accept electrical and magnetic forces as different. In this conception, we couldn't have understood magnetic induction of current, what is light, etc. Only when Maxwell unified the previous knowledge, mainly from Faraday, by using the concept of lines of force whose variations can produce other other types of interaction (electric to magnetic and vice-versa). Still this is not more fundamental, it is a better description for the mentioned phenomena, but is not a better description for classical gravitation or statics laws.
Finally, the concept of force cannot be used in General Relativity and Quantum Mechanics.
GR considers gravitation not as a force, but as a phenomenon resulting from the simple movement in a 4D space (3D space plus time).
QM cannot describe particles as points following trajectories defined by forces, because all of those concepts give answers not observed in reality, and therefore wrong.
Still non is more fundamental, but yes maybe more inclusive, as GR can contain classical gravitation, and QED can contain ED.
Answer to comment: So can we define a quantity named "Field" independent of the quantity "Force" and also independent of the "Nature of the field/force" weather being gravitational, electric, etc and then deduce these specific fields as a special case of the first quantity? And if this is true, how can we define it?(consider I want a definition in classical mechanics)
No, this is not possible. The definition of field is based on the definition of force and interaction. As I mention above, the phenomena in Gravitation, Electrostatics and Magnetostatics have all a similar formulation of force and do not require field necessarily. Example of this are that laws like Gauss Law apply to all of them because the form of the force is equivalent.
But when it comes to Electrodynamics and Gravitodynamics, the analogy does not amount to be an equivalency (see Gravitoelectromagnetism).
As for Quantum theories, the "field" while still being used formally, the concept is very different, because the classical idea of force is inapplicable (as trajectories and positions are meaningless, rendering the concept of inertia useless). Hence a quantum field is completely different than the classical field, the only common thing is the name* (see QFT)
*Note: Yes the have Hamiltonian and Lagrangian formulations, but the mathematical framework and objects are different and have no more connection with the concepts of classical mechanics, than the relation between classical and quantum momentum or position.