We propose a novel multi-tier (top, intermediate, and bottom tiers) architecture at the edge of a heterogeneous network (HetNet) where non-orthogonal multiple access (NOMA) provides access to user equipment (UE) to participate in federated edge learning (FEL). The HetNet consists of a macro base station (MBS) and several small base stations (SBSs) where each BS is equipped with an edge server (ES). SBSs use the same system bandwidth to increase the system capacity. The top tier consists of the MBS-ES which works as the global model aggregator while ESs of SBSs and UEs connected with MBS reside in the intermediate tier. Similarly, UEs connected with an SBS-ES of the intermediate tier occupy the bottom tier. ESs of SBSs work as the intermediate model aggregators between the ES of the top tier and the UEs of the bottom tier. To minimize the total energy consumption (EC) for local computing (LC) and uplink transmission (UT) of UEs, we formulate a non-linear programming (NLP) optimization problem, present our solution by decomposing the problem into sub-problems, and propose two sequential algorithms to estimate EC for both LC and UT with less complexity. Our extensively simulated results demonstrate the viability of our proposed work.