Building automatic speech recognition (ASR) systems is a challenging task, especially for under-resourced languages that need to construct corpora nearly from scratch and lack sufficient training data. It has emerged that several African indigenous languages, including Kiswahili, are technologically under-resourced. ASR systems are crucial, particularly for the hearing-impaired persons who can benefit from having transcripts in their native languages. However, the absence of transcribed speech datasets has complicated efforts to develop ASR models for these indigenous languages. This paper explores the transcription process and the development of a Kiswahili speech corpus, which includes both read-out texts and spontaneous speech data from native Kiswahili speakers. The study also discusses the vowels and consonants in Kiswahili and provides an updated Kiswahili phoneme dictionary for the ASR model that was created using the CMU Sphinx speech recognition toolbox, an open-source speech recognition toolkit. The ASR model was trained using an extended phonetic set that yielded a WER and SER of 18.87% and 49.5%, respectively, an improved performance than previous similar research for under-resourced languages.