In the present article we analyze the matter-geometry coupled f(Q, T) theory of gravity. We offer the fully covariant formulation of the theory, with which we construct the correct energy balance equation and employ it to conduct a dynamical system analysis in a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime. We consider three different functional forms of the f(Q, T) function, specifically, $$f(Q,T)=\alpha Q+ \beta T$$
f
(
Q
,
T
)
=
α
Q
+
β
T
, $$f(Q,T)=\alpha Q+ \beta T^2$$
f
(
Q
,
T
)
=
α
Q
+
β
T
2
, and $$f(Q,T)=Q+ \alpha Q^2+ \beta T$$
f
(
Q
,
T
)
=
Q
+
α
Q
2
+
β
T
. We attempt to investigate the physical capabilities of these models to describe various cosmological epochs. We calculate Friedmann-like equations in each case and introduce some phase space variables to simplify the equations in more concise forms. We observe that the linear model $$f(Q,T)=\alpha Q+ \beta T$$
f
(
Q
,
T
)
=
α
Q
+
β
T
with $$\beta =0$$
β
=
0
is completely equivalent to the GR case without cosmological constant $$\Lambda $$
Λ
. Further, we find that the model $$f(Q,T)=\alpha Q+ \beta T^2$$
f
(
Q
,
T
)
=
α
Q
+
β
T
2
with $$\beta \ne 0$$
β
≠
0
successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model $$f(Q,T)= Q+ \alpha Q^2+ \beta T$$
f
(
Q
,
T
)
=
Q
+
α
Q
2
+
β
T
with $$\alpha \ne 0$$
α
≠
0
represents an accelerated de-Sitter epoch for the constraints $$\beta < -1$$
β
<
-
1
or $$ \beta \ge 0$$
β
≥
0
.