Methyltransferase that catalyzes the formation of N(1)-methyladenine at position 58 (m1A58) in various tRNAs in mitochondrion, including tRNA(Leu) (deciphering codons UUA or UUG), tRNA(Lys) and tRNA(Ser) (deciphering codons UCA, UCU, UCG or UCC) (PubMed:23097428). Catalyzes the formation of 1-methyladenosine at position 947 of mitochondrial 16S ribosomal RNA and this modification is most likely important for mitoribosomal structure and function (PubMed:27631568). In addition to tRNA N(1)-methyltransferase activity, also acts as a mRNA N(1)-methyltransferase by mediating methylation of adenosine residues at the N(1) position of MT-ND5 mRNA, leading to interfere with mitochondrial translation (PubMed:29107537). adenosine(58) in tRNA + S-adenosyl-L-methionine = H(+) + N(1)-methyladenosine(58) in tRNA + S-adenosyl-L-homocysteine an adenosine in mRNA + S-adenosyl-L-methionine = an N(1)-methyladenosine in mRNA + H(+) + S-adenosyl-L-homocysteine Homooligomer; in contrast to TRMT61A, does not form a heterotetramer. Belongs to the class I-like SAM-binding methyltransferase superfamily. TRM61 family. The identity of the enzyme catalyzing mitochondrial mRNA N(1)-methyltransferase is unclear. According to a report, mitochondrial mRNA N(1)-methyltransferase activity is catalyzed by TRMT61B (PubMed:29107537). According to a second report, it is mediated by TRMT10C (AC Q7L0Y3) (PubMed:29072297). As both reports only tested one protein (either TRMT61B or TRMT10C), it is possible that both proteins have this activity.