Digital Twins (DT) virtually model cyber-physical objects using Internet of Things (IoT) components (e.g., sensors) to gather and process senstive information stored in the cloud. Trustworthiness of the streamed data is crucial which requires quantum safety and breach resiliency. Digital signatures are essential for scalable authentication and non-repudiation. Yet, NIST PQC signature standards are exorbitantly costly for low-end IoT without considering forward security. Moreover, Post-Quantum (PQ) signatures lack aggregation, which is highly desirable to reduce the transmission and storage burdens in DTs. Hence, there is an urgent need for lightweight digital signatures that offer compromise resiliency and compactness while permitting an effective transition into the PQ era for DTs. We create a series of highly lightweight digital signatures called Hardware-ASsisted Efficient Signature (HASES) that meets the above requirements. The core of HASES is a hardware-assisted cryptographic commitment construct oracle (CCO) that permits verifiers to obtain expensive commitments without signer interaction. We created three HASES schemes: PQ-HASES is a forward-secure PQ signature, LA-HASES is an efficient aggregate Elliptic-Curve signature, and HY-HASES is a novel hybrid scheme that combines PQ-HASES and LA-HASES with novel strong nesting and sequential aggregation. HASES does not require a secure-hardware on the signer. We proved that HASES schemes are secure and implemented them on commodity hardware and an 8-bit AVR ATmega2560. Our experiments confirm that PQ-HASES and LA-HASES are two magnitudes of times more signer efficient than their PQ and conventional-secure counterparts, respectively. HY-HASES outperforms NIST PQC and conventional signature combinations, offering a standardcompliant transitional solution for emerging DTs. We open-source HASES schemes for public testing and adaptation.