In the IEEE 802.11ax standard, a mode of operation called target wake time (TWT) is introduced towards enabling deterministic scheduling in WLAN networks. In the TWT mode, a group of stations (STAs) can negotiate with the access point (AP) a periodically repeating time window, referred to as TWT Service Period (TWT-SP), over which they are awake and outside which they sleep for saving power. The offset from a common starting time to the first TWT-SP is referred to as the TWT Offset (TWT-O) and the periodicity of TWT-SP is referred to as the TWT Wake Interval (TWT-WI). In this work, we consider communication between multiple STAs with heterogeneous traffic flows and an AP of an IEEE 802.11ax network operating in the TWT mode. Our objective is to maximize a long-term weighted average timely throughput across the STAs, where the instantaneous timely throughput is defined as the number of packets delivered successfully before their deadlines at a decision instant. To achieve this, we obtain algorithms, composed of (i) an inner resource allocation (RA) routine that allocates resource units (RUs) and transmit powers to STAs, and (ii) an outer grouping routine that assigns STAs to (TWT-SP, TWT-O, TWT-WI) triplets. For inner RA, we propose a near-optimal low-complexity algorithm using the drift-plus-penalty (DPP) framework and we adopt a greedy algorithm as outer grouping routine. Via numerical simulations, we observe that the proposed algorithm, composed of a DPP based RA and a greedy grouping routine, performs better than other competitive algorithms.